Filnix wiki

x :

xs :

listZ

⊢

lstp x :: xs ⊣⊢ ∃b : Z nx : ptr, ⌜node_okp b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 x ∗ lstnx xs

reflexivity

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

reflexivity

A segment to q and the node at q make a segment to the node's next pointer.

241Lemma lseg_snoc

∀ p q ys b nx y

lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

Explore proof 12 tactics

Initial goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p, q :

ys :

listZ

b :

nx :

y :

⊢

node_okq b → lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

intros Hq

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p, q :

ys :

listZ

b :

nx :

y :

Hq :

⊢

lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

revert p

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

ys :

listZ

b :

nx :

y :

Hq :

⊢

∀p : ptr, lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

induction ys as | y′ ys IH ; intros p ; cbn [ lseg app ]

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

b :

nx :

y :

Hq :

p :

⊢

⌜p = q⌝ −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ ∃b₀ : Z nx₀ : ptr, ⌜node_okp b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 y ∗ ⌜nx₀ = nx⌝

focused goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y′ :

ys :

listZ

b :

nx :

y :

Hq :

IH :

∀p : ptr, lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

p :

⊢

∃b₀ : Z nx₀ : ptr, ⌜node_okp b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 y′ ∗ lsegnx₀ q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ ∃b₀ : Z nx₀ : ptr, ⌜node_okp b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 y′ ∗ lsegnx₀ nx ys ++ y

–iIntros → Hl Hp Hi

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

b :

nx :

y :

Hq :

Hl :

Hp :

pcellb 0 nx

Hi :

icellb 8 y

∗

∃b₀ : Z nx₀ : ptr, ⌜node_okq b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 y ∗ ⌜nx₀ = nx⌝

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y′ :

ys :

listZ

b :

nx :

y :

Hq :

IH :

∀p : ptr, lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

p :

⊢

iExists b, nx

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

b :

nx :

y :

Hq :

Hl :

Hp :

pcellb 0 nx

Hi :

icellb 8 y

∗

⌜node_okq b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 y ∗ ⌜nx = nx⌝

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y′ :

ys :

listZ

b :

nx :

y :

Hq :

IH :

∀p : ptr, lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

p :

⊢

by iFrame

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y′ :

ys :

listZ

b :

nx :

y :

Hq :

IH :

∀p : ptr, lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

p :

⊢

–iIntros Hs Hl Hp Hi

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y′ :

ys :

listZ

b :

nx :

y :

Hq :

IH :

∀p : ptr, lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

p :

Hs :

∃b₀ : Z nx₀ : ptr, ⌜node_okp b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 y′ ∗ lsegnx₀ q ys

Hl :

Hp :

pcellb 0 nx

Hi :

icellb 8 y

∗

∃b₀ : Z nx₀ : ptr, ⌜node_okp b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 y′ ∗ lsegnx₀ nx ys ++ y

iDestruct Hs as b′ nx′ (% & Hl′ & Hp′ & Hi′ & Hs)

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y′ :

ys :

listZ

b :

nx :

y :

Hq :

IH :

∀p : ptr, lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

p :

b′ :

nx′ :

H :

node_okp b′

Hl′ :

liveb′ node_regb′

Hp′ :

pcellb′ 0 nx′

Hi′ :

icellb′ 8 y′

Hs :

lsegnx′ q ys

Hl :

Hp :

pcellb 0 nx

Hi :

icellb 8 y

∗

∃b₀ : Z nx₀ : ptr, ⌜node_okp b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 y′ ∗ lsegnx₀ nx ys ++ y

iExists b′, nx′

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y′ :

ys :

listZ

b :

nx :

y :

Hq :

IH :

∀p : ptr, lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

p :

b′ :

nx′ :

H :

node_okp b′

Hl′ :

liveb′ node_regb′

Hp′ :

pcellb′ 0 nx′

Hi′ :

icellb′ 8 y′

Hs :

lsegnx′ q ys

Hl :

Hp :

pcellb 0 nx

Hi :

icellb 8 y

∗

⌜node_okp b′⌝ ∗ liveb′ node_regb′ ∗ pcellb′ 0 nx′ ∗ icellb′ 8 y′ ∗ lsegnx′ nx ys ++ y

iFrame Hl′ Hp′ Hi′

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y′ :

ys :

listZ

b :

nx :

y :

Hq :

IH :

∀p : ptr, lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

p :

b′ :

nx′ :

H :

node_okp b′

Hs :

lsegnx′ q ys

Hl :

Hp :

pcellb 0 nx

Hi :

icellb 8 y

∗

⌜node_okp b′⌝ ∗ lsegnx′ nx ys ++ y

iSplit ; done |

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y′ :

ys :

listZ

b :

nx :

y :

Hq :

IH :

∀p : ptr, lsegp q ys −∗ liveb node_regb −∗ pcellb 0 nx −∗ icellb 8 y −∗ lsegp nx ys ++ y

p :

b′ :

nx′ :

H :

node_okp b′

Hs :

lsegnx′ q ys

Hl :

Hp :

pcellb 0 nx

Hi :

icellb 8 y

∗

lsegnx′ nx ys ++ y

iApply IH with Hs Hl Hp Hi

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

intros Hq

revert p

induction ys as | y′ ys IH ; intros p ; cbn [ lseg app ]

–iIntros → Hl Hp Hi

iExists b, nx

by iFrame

–iIntros Hs Hl Hp Hi

iDestruct Hs as b′ nx′ (% & Hl′ & Hp′ & Hi′ & Hs)

iExists b′, nx′

iFrame Hl′ Hp′ Hi′

iSplit ; done |

iApply IH with Hs Hl Hp Hi

A segment to q and the list from q make the list from p.

252Lemma lseg_lst

∀ p q ys zs

lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

Explore proof 11 tactics

Initial goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p, q :

ys, zs :

listZ

⊢

lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

revert p

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

ys, zs :

listZ

⊢

∀p : ptr, lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

induction ys as | y ys IH ; intros p ; cbn [ lseg app ]

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

zs :

listZ

p :

⊢

⌜p = q⌝ −∗ lstq zs −∗ lstp zs

focused goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y :

ys, zs :

listZ

IH :

∀p : ptr, lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

p :

⊢

∃b : Z nx : ptr, ⌜node_okp b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 y ∗ lsegnx q ys −∗ lstq zs −∗ lstp y :: ys ++ zs

–iIntros → Hl

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

zs :

listZ

Hl :

lstq zs

∗

lstq zs

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y :

ys, zs :

listZ

IH :

∀p : ptr, lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

p :

⊢

∃b : Z nx : ptr, ⌜node_okp b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 y ∗ lsegnx q ys −∗ lstq zs −∗ lstp y :: ys ++ zs

iExact Hl

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y :

ys, zs :

listZ

IH :

∀p : ptr, lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

p :

⊢

∃b : Z nx : ptr, ⌜node_okp b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 y ∗ lsegnx q ys −∗ lstq zs −∗ lstp y :: ys ++ zs

–iIntros Hs Hl

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y :

ys, zs :

listZ

IH :

∀p : ptr, lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

p :

Hs :

∃b : Z nx : ptr, ⌜node_okp b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 y ∗ lsegnx q ys

Hl :

lstq zs

∗

lstp y :: ys ++ zs

iDestruct Hs as b nx (% & Hlv & Hp & Hi & Hs)

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y :

ys, zs :

listZ

IH :

∀p : ptr, lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

p :

b :

nx :

H :

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 y

Hs :

lsegnx q ys

Hl :

lstq zs

∗

lstp y :: ys ++ zs

cbn [ lst ]

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y :

ys, zs :

listZ

IH :

∀p : ptr, lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

p :

b :

nx :

H :

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 y

Hs :

lsegnx q ys

Hl :

lstq zs

∗

∃b₀ : Z nx₀ : ptr, ⌜node_okp b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 y ∗ lstnx₀ ys ++ zs

iExists b, nx

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y :

ys, zs :

listZ

IH :

∀p : ptr, lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

p :

b :

nx :

H :

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 y

Hs :

lsegnx q ys

Hl :

lstq zs

∗

⌜node_okp b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 y ∗ lstnx ys ++ zs

iFrame Hlv Hp Hi

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y :

ys, zs :

listZ

IH :

∀p : ptr, lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

p :

b :

nx :

H :

Hs :

lsegnx q ys

Hl :

lstq zs

∗

⌜node_okp b⌝ ∗ lstnx ys ++ zs

iSplit ; done |

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

q :

y :

ys, zs :

listZ

IH :

∀p : ptr, lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs

p :

b :

nx :

H :

Hs :

lsegnx q ys

Hl :

lstq zs

∗

lstnx ys ++ zs

iApply IH with Hs Hl

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

revert p

induction ys as | y ys IH ; intros p ; cbn [ lseg app ]

–iIntros → Hl

iExact Hl

–iIntros Hs Hl

iDestruct Hs as b nx (% & Hlv & Hp & Hi & Hs)

cbn [ lst ]

iExists b, nx

iFrame Hlv Hp Hi

iSplit ; done |

iApply IH with Hs Hl

The head of a list: its address is in range, and the life of the object its capability names, if any, can be lent out.

262Lemma lst_cap

∀ p xs

lstp xs −∗ ⌜0 ≤ ptr_addrp < 2 ^ 64⌝ ∗ live_capptr_capp node_regptr_addrp ∗ live_capptr_capp node_regptr_addrp −∗ lstp xs

Explore proof 16 tactics

Initial goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

xs :

listZ

⊢

lstp xs −∗ ⌜0 ≤ ptr_addrp < 2 ^ 64⌝ ∗ live_capptr_capp node_regptr_addrp ∗ live_capptr_capp node_regptr_addrp −∗ lstp xs

destruct xs as | x xs ; cbn [ lst ]

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

⊢

⌜p = null⌝ −∗ ⌜0 ≤ ptr_addrp < 2 ^ 64⌝ ∗ live_capptr_capp node_regptr_addrp ∗ live_capptr_capp node_regptr_addrp −∗ ⌜p = null⌝

focused goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

x :

xs :

listZ

⊢

∃b : Z nx : ptr, ⌜node_okp b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 x ∗ lstnx xs −∗ ⌜0 ≤ ptr_addrp < 2 ^ 64⌝ ∗ live_capptr_capp node_regptr_addrp ∗ live_capptr_capp node_regptr_addrp −∗ ∃b : Z nx : ptr, ⌜node_okp b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 x ∗ lstnx xs

–iIntros →

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

∗

⌜0 ≤ ptr_addrnull < 2 ^ 64⌝ ∗ live_capptr_capnull node_regptr_addrnull ∗ live_capptr_capnull node_regptr_addrnull −∗ ⌜null = null⌝

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

x :

xs :

listZ

⊢

cbn

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

∗

⌜0 ≤ 0 < 2 ^ 64⌝ ∗ True ∗ True −∗ ⌜null = null⌝

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

x :

xs :

listZ

⊢

iSplit ; iPureIntro ; lia |

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

∗

True ∗ True −∗ ⌜null = null⌝

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

x :

xs :

listZ

⊢

iSplit ; done |

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

∗

True −∗ ⌜null = null⌝

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

x :

xs :

listZ

⊢

by iIntros _

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

x :

xs :

listZ

⊢

–iIntros H

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

x :

xs :

listZ

H :

∃b : Z nx : ptr, ⌜node_okp b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 x ∗ lstnx xs

∗

⌜0 ≤ ptr_addrp < 2 ^ 64⌝ ∗ live_capptr_capp node_regptr_addrp ∗ live_capptr_capp node_regptr_addrp −∗ ∃b : Z nx : ptr, ⌜node_okp b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 x ∗ lstnx xs

iDestruct H as b nx Hn (Hlv & Hp & Hi & Hl)

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

x :

xs :

listZ

b :

nx :

Hn :

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 x

Hl :

lstnx xs

∗

⌜0 ≤ ptr_addrp < 2 ^ 64⌝ ∗ live_capptr_capp node_regptr_addrp ∗ live_capptr_capp node_regptr_addrp −∗ ∃b₀ : Z nx₀ : ptr, ⌜node_okp b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 x ∗ lstnx₀ xs

destruct Hn as → & Hb₀ & Hb₁ & Hb₂

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

x :

xs :

listZ

b :

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 x

Hl :

lstnx xs

∗

⌜0 ≤ ptr_addrptr_addr ≔ b; ptr_cap ≔ Objb < 2 ^ 64⌝ ∗ live_capptr_capptr_addr ≔ b; ptr_cap ≔ Objb node_regptr_addrptr_addr ≔ b; ptr_cap ≔ Objb ∗ live_capptr_capptr_addr ≔ b; ptr_cap ≔ Objb node_regptr_addrptr_addr ≔ b; ptr_cap ≔ Objb −∗ ∃b₀ : Z nx₀ : ptr, ⌜node_okptr_addr ≔ b; ptr_cap ≔ Objb b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 x ∗ lstnx₀ xs

cbn [ ptr_addr ptr_cap live_cap ]

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

x :

xs :

listZ

b :

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 x

Hl :

lstnx xs

∗

⌜0 ≤ b < 2 ^ 64⌝ ∗ liveb node_regb ∗ liveb node_regb −∗ ∃b₀ : Z nx₀ : ptr, ⌜node_okptr_addr ≔ b; ptr_cap ≔ Objb b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 x ∗ lstnx₀ xs

iSplit ; iPureIntro ; lia |

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

x :

xs :

listZ

b :

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 x

Hl :

lstnx xs

∗

liveb node_regb ∗ liveb node_regb −∗ ∃b₀ : Z nx₀ : ptr, ⌜node_okptr_addr ≔ b; ptr_cap ≔ Objb b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 x ∗ lstnx₀ xs

iFrame Hlv

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

x :

xs :

listZ

b :

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

Hp :

pcellb 0 nx

Hi :

icellb 8 x

Hl :

lstnx xs

∗

liveb node_regb −∗ ∃b₀ : Z nx₀ : ptr, ⌜node_okptr_addr ≔ b; ptr_cap ≔ Objb b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 x ∗ lstnx₀ xs

iIntros Hlv

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

x :

xs :

listZ

b :

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

Hp :

pcellb 0 nx

Hi :

icellb 8 x

Hl :

lstnx xs

Hlv :

∗

∃b₀ : Z nx₀ : ptr, ⌜node_okptr_addr ≔ b; ptr_cap ≔ Objb b₀⌝ ∗ liveb₀ node_regb₀ ∗ pcellb₀ 0 nx₀ ∗ icellb₀ 8 x ∗ lstnx₀ xs

iExists b, nx

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

x :

xs :

listZ

b :

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

Hp :

pcellb 0 nx

Hi :

icellb 8 x

Hl :

lstnx xs

Hlv :

∗

⌜node_okptr_addr ≔ b; ptr_cap ≔ Objb b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 x ∗ lstnx xs

iFrame

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

x :

xs :

listZ

b :

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

∗

⌜node_okptr_addr ≔ b; ptr_cap ≔ Objb b⌝

done

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

destruct xs as | x xs ; cbn [ lst ]

–iIntros →

cbn

iSplit ; iPureIntro ; lia |

iSplit ; done |

by iIntros _

–iIntros H

iDestruct H as b nx Hn (Hlv & Hp & Hi & Hl)

destruct Hn as → & Hb₀ & Hb₁ & Hb₂

cbn [ ptr_addr ptr_cap live_cap ]

iSplit ; iPureIntro ; lia |

iFrame Hlv

iIntros Hlv

iExists b, nx

iFrame

done

sum's loop, from the point after its head's phis, with the walked prefix ys as a segment from p to q, the rest zs as the list from q, pr.1 holding q and pr.2 the prefix's sum: the run returns the whole list's sum and hands the list back. By Löb induction.

277Lemma sum_loop

∀ p Φ

⊢ ∀e q ys zs, ⌜lookupTAtom"pr.1" e = SomeWPtrq ∧ lookupTAtom"pr.2" e = SomeWIntlist_sumys⌝ −∗ lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs −∗ ΦRetWIntlist_sumys ++ zs −∗ WPERunmkFramels_fn"sum" e [ ] None ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 : lexpr {Φ}

Explore proof 43 tactics

Initial goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

⊢

⊢ ∀e : listname × word q : ptr ys zs : listZ, ⌜lookupTAtom"pr.1" e = SomeWPtrq ∧ lookupTAtom"pr.2" e = SomeWIntlist_sumys⌝ −∗ lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs −∗ ΦRetWIntlist_sumys ++ zs −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 : lexpr {v. Φv}

iLöb as IH

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

IH :

▷∀e : listname × word q : ptr ys zs : listZ, ⌜lookupTAtom"pr.1" e = SomeWPtrq ∧ lookupTAtom"pr.2" e = SomeWIntlist_sumys⌝ −∗ lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs −∗ ΦRetWIntlist_sumys ++ zs −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

□

∀e : listname × word q : ptr ys zs : listZ, ⌜lookupTAtom"pr.1" e = SomeWPtrq ∧ lookupTAtom"pr.2" e = SomeWIntlist_sumys⌝ −∗ lsegp q ys −∗ lstq zs −∗ lstp ys ++ zs −∗ ΦRetWIntlist_sumys ++ zs −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

iIntros e q ys zs Hq Hs Hs Hl HΦ

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys, zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

IH :

▷∀e₀ : listname × word q₀ : ptr ys₀ zs₀ : listZ, ⌜lookupTAtom"pr.1" e₀ = SomeWPtrq₀ ∧ lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys₀⌝ −∗ lsegp q₀ ys₀ −∗ lstq₀ zs₀ −∗ lstp ys₀ ++ zs₀ −∗ ΦRetWIntlist_sumys₀ ++ zs₀ −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

□

Hs :

lsegp q ys

Hl :

lstq zs

HΦ :

lstp ys ++ zs −∗ ΦRetWIntlist_sumys ++ zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

pose proof list_sum_rangeys

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys, zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq zs

HΦ :

lstp ys ++ zs −∗ ΦRetWIntlist_sumys ++ zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

destruct zs as | z zs

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

▷∀e₀ : listname × word q₀ : ptr ys₀ zs : listZ, ⌜lookupTAtom"pr.1" e₀ = SomeWPtrq₀ ∧ lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys₀⌝ −∗ lsegp q₀ ys₀ −∗ lstq₀ zs −∗ lstp ys₀ ++ zs −∗ ΦRetWIntlist_sumys₀ ++ zs −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

□

Hs :

lsegp q ys

Hl :

lstq [ ]

HΦ :

lstp ys ++ [ ] −∗ ΦRetWIntlist_sumys ++ [ ]

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

focused goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

–iDestruct Hl as %→

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

ys :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrnull

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

▷∀e₀ : listname × word q : ptr ys₀ zs : listZ, ⌜lookupTAtom"pr.1" e₀ = SomeWPtrq ∧ lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys₀⌝ −∗ lsegp q ys₀ −∗ lstq zs −∗ lstp ys₀ ++ zs −∗ ΦRetWIntlist_sumys₀ ++ zs −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

□

Hs :

lsegp null ys

HΦ :

lstp ys ++ [ ] −∗ ΦRetWIntlist_sumys ++ [ ]

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

cbn [ sum_L3 b_insts b_jump ]

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

ys :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrnull

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp null ys

HΦ :

lstp ys ++ [ ] −∗ ΦRetWIntlist_sumys ++ [ ]

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" LetTAtom"v7" L Ptoi TmpTAtom"pr.1"; LetTAtom"v8" W CmpNe L TmpTAtom"v7"; Const0 JBranchTmpTAtom"v8" ToTAtom"L4" ToTAtom"L5" {v. Φv}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

ls_facts

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

ys :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrnull

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

IH :

□

Hs :

lsegp null ys

HΦ :

lstp ys ++ [ ] −∗ ΦRetWIntlist_sumys ++ [ ]

∗

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

rewrite app_nil_r

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

ys :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrnull

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

IH :

□

Hs :

lsegp null ys

HΦ :

lstp ys −∗ ΦRetWIntlist_sumys

∗

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

wp_let_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

H :

0 ≤ list_sumys < 2 ^ 64

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e₀ :

listname × word

Hput :

lookupTAtom"v7" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrnull

IH :

∀e : listname × word q : ptr ys₀ zs : listZ, ⌜lookupTAtom"pr.1" e = SomeWPtrq ∧ lookupTAtom"pr.2" e = SomeWIntlist_sumys₀⌝ −∗ lsegp q ys₀ −∗ lstq zs −∗ lstp ys₀ ++ zs −∗ ΦRetWIntlist_sumys₀ ++ zs −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" LetTAtom"v7" L Ptoi TmpTAtom"pr.1"; LetTAtom"v8" W CmpNe L TmpTAtom"v7"; Const0 JBranchTmpTAtom"v8" ToTAtom"L4" ToTAtom"L5" {v. Φv}

□

Hs :

lsegp null ys

HΦ :

lstp ys −∗ ΦRetWIntlist_sumys

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" LetTAtom"v8" W CmpNe L TmpTAtom"v7"; Const0 JBranchTmpTAtom"v8" ToTAtom"L4" ToTAtom"L5" {v. Φv}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

wp_let_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

H :

0 ≤ list_sumys < 2 ^ 64

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v8" e = SomeWInt0

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrnull

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWInt0

IH :

∀e₀ : listname × word q : ptr ys₀ zs : listZ, ⌜lookupTAtom"pr.1" e₀ = SomeWPtrq ∧ lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys₀⌝ −∗ lsegp q ys₀ −∗ lstq zs −∗ lstp ys₀ ++ zs −∗ ΦRetWIntlist_sumys₀ ++ zs −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" LetTAtom"v7" L Ptoi TmpTAtom"pr.1"; LetTAtom"v8" W CmpNe L TmpTAtom"v7"; Const0 JBranchTmpTAtom"v8" ToTAtom"L4" ToTAtom"L5" {v. Φv}

□

Hs :

lsegp null ys

HΦ :

lstp ys −∗ ΦRetWIntlist_sumys

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" [ ] JBranchTmpTAtom"v8" ToTAtom"L4" ToTAtom"L5" {v. Φv}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

wp_branch_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

H :

0 ≤ list_sumys < 2 ^ 64

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v8" e = SomeWInt0

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrnull

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWInt0

IH :

□

Hs :

lsegp null ys

HΦ :

lstp ys −∗ ΦRetWIntlist_sumys

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"L5" SomeTAtom"L3" {v. Φv}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

wp_enter_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

H :

0 ≤ list_sumys < 2 ^ 64

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v8" e = SomeWInt0

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrnull

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWInt0

IH :

□

Hs :

lsegp null ys

HΦ :

lstp ys −∗ ΦRetWIntlist_sumys

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L5" [ ] JRetTmpTAtom"pr.2" {v. Φv}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

iApply wp_ret ; first side | iNext

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

H :

0 ≤ list_sumys < 2 ^ 64

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v8" e = SomeWInt0

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrnull

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWInt0

IH :

□

Hs :

lsegp null ys

HΦ :

lstp ys −∗ ΦRetWIntlist_sumys

∗

ΦRetWIntlist_sumys

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

iApply HΦ

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

H :

0 ≤ list_sumys < 2 ^ 64

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v8" e = SomeWInt0

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrnull

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWInt0

IH :

□

Hs :

lsegp null ys

∗

lstp ys

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

iDestruct lseg_lst_ _ _ [ ] with Hs [//] as H

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

H :

0 ≤ list_sumys < 2 ^ 64

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v8" e = SomeWInt0

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrnull

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWInt0

IH :

□

H :

lstp ys ++ [ ]

∗

lstp ys

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

rewrite app_nil_r

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

H :

0 ≤ list_sumys < 2 ^ 64

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v8" e = SomeWInt0

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrnull

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWInt0

IH :

□

H :

lstp ys

∗

lstp ys

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

iExact H

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

lstq z :: zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

–rewrite lst_cons

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

q :

ys :

listZ

z :

zs :

listZ

Hq :

lookupTAtom"pr.1" e = SomeWPtrq

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

IH :

□

Hs :

lsegp q ys

Hl :

∃b : Z nx : ptr, ⌜node_okq b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 z ∗ lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

iDestruct Hl as b nx → & Hb₀ & Hb₁ & Hb₂ (Hlv & Hp & Hi & Hl)

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

ys :

listZ

z :

zs :

listZ

b :

Hq :

lookupTAtom"pr.1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

IH :

▷∀e₀ : listname × word q : ptr ys₀ zs₀ : listZ, ⌜lookupTAtom"pr.1" e₀ = SomeWPtrq ∧ lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys₀⌝ −∗ lsegp q ys₀ −∗ lstq zs₀ −∗ lstp ys₀ ++ zs₀ −∗ ΦRetWIntlist_sumys₀ ++ zs₀ −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

ls_facts

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

ys :

listZ

z :

zs :

listZ

b :

Hq :

lookupTAtom"pr.1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" b_instssum_L3 b_jumpsum_L3 {v. Φv}

cbn [ sum_L3 b_insts b_jump ]

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

e :

listname × word

ys :

listZ

z :

zs :

listZ

b :

Hq :

lookupTAtom"pr.1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

Hs :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

wp_let_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e₀ :

listname × word

Hput :

lookupTAtom"v7" e₀ = SomeWIntb

H₁₀ :

lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

IH :

∀e : listname × word q : ptr ys₀ zs₀ : listZ, ⌜lookupTAtom"pr.1" e = SomeWPtrq ∧ lookupTAtom"pr.2" e = SomeWIntlist_sumys₀⌝ −∗ lsegp q ys₀ −∗ lstq zs₀ −∗ lstp ys₀ ++ zs₀ −∗ ΦRetWIntlist_sumys₀ ++ zs₀ −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" LetTAtom"v7" L Ptoi TmpTAtom"pr.1"; LetTAtom"v8" W CmpNe L TmpTAtom"v7"; Const0 JBranchTmpTAtom"v8" ToTAtom"L4" ToTAtom"L5" {v. Φv}

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

wp_let_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v8" e = SomeWInt1

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

IH :

∀e₀ : listname × word q : ptr ys₀ zs₀ : listZ, ⌜lookupTAtom"pr.1" e₀ = SomeWPtrq ∧ lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys₀⌝ −∗ lsegp q ys₀ −∗ lstq zs₀ −∗ lstp ys₀ ++ zs₀ −∗ ΦRetWIntlist_sumys₀ ++ zs₀ −∗ WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" LetTAtom"v7" L Ptoi TmpTAtom"pr.1"; LetTAtom"v8" W CmpNe L TmpTAtom"v7"; Const0 JBranchTmpTAtom"v8" ToTAtom"L4" ToTAtom"L5" {v. Φv}

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" [ ] JBranchTmpTAtom"v8" ToTAtom"L4" ToTAtom"L5" {v. Φv}

wp_branch_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v8" e = SomeWInt1

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"L4" SomeTAtom"L3" {v. Φv}

wp_enter_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v8" e = SomeWInt1

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" FlightTAtom"v11" Add FAddressTmpTAtom"pr.1"; FValueConst8 LowerOfTmpTAtom"pr.1"; LetTAtom"chk0" A Check0 8 Read 1 TmpTAtom"v11"; LetTAtom"v12" L RawLoadLdL 0 TmpTAtom"chk0"; LetTAtom"v13" L Add TmpTAtom"pr.2"; TmpTAtom"v12"; LetTAtom"chk1" A HalfCheckLower 0 8 Read 8 TmpTAtom"chk0"; TmpTAtom"pr.1"; LetTAtom"v15" P RawLoadPointer0 AuxRead; LowerResolve; AddressRead TmpTAtom"chk1" JGotoPollTAtom"L3" {v. Φv}

wp_flight_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e₀ :

listname × word

Hput :

lookupTAtom"v11" e₀ = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v7" e₀ = SomeWIntb

H₁₀ :

lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e₀ = SomeWInt1

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" LetTAtom"chk0" A Check0 8 Read 1 TmpTAtom"v11"; LetTAtom"v12" L RawLoadLdL 0 TmpTAtom"chk0"; LetTAtom"v13" L Add TmpTAtom"pr.2"; TmpTAtom"v12"; LetTAtom"chk1" A HalfCheckLower 0 8 Read 8 TmpTAtom"chk0"; TmpTAtom"pr.1"; LetTAtom"v15" P RawLoadPointer0 AuxRead; LowerResolve; AddressRead TmpTAtom"chk1" JGotoPollTAtom"L3" {v. Φv}

iApply wp_check with Hlv ; first side | iNext ; iIntros Hlv ; gen_env

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₄ :

lookupTAtom"v8" e = SomeWInt1

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₃ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hp :

pcellb 0 nx

Hi :

icellb 8 z

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

Hlv :

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" LetTAtom"v12" L RawLoadLdL 0 TmpTAtom"chk0"; LetTAtom"v13" L Add TmpTAtom"pr.2"; TmpTAtom"v12"; LetTAtom"chk1" A HalfCheckLower 0 8 Read 8 TmpTAtom"chk0"; TmpTAtom"pr.1"; LetTAtom"v15" P RawLoadPointer0 AuxRead; LowerResolve; AddressRead TmpTAtom"chk1" JGotoPollTAtom"L3" {v. Φv}

iApply wp_raw_load with Hlv Hi ; first side | iNext ; iIntros Hlv Hi ; gen_env

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e₀ :

listname × word

Hput :

lookupTAtom"v12" e₀ = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"v11" e₀ = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v7" e₀ = SomeWIntb

H₁₀ :

lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e₀ = SomeWInt1

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hp :

pcellb 0 nx

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

Hlv :

Hi :

icellb 8 z

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" LetTAtom"v13" L Add TmpTAtom"pr.2"; TmpTAtom"v12"; LetTAtom"chk1" A HalfCheckLower 0 8 Read 8 TmpTAtom"chk0"; TmpTAtom"pr.1"; LetTAtom"v15" P RawLoadPointer0 AuxRead; LowerResolve; AddressRead TmpTAtom"chk1" JGotoPollTAtom"L3" {v. Φv}

wp_let_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e :

listname × word

Hput₀ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₆ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₄ :

lookupTAtom"v8" e = SomeWInt1

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₃ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₅ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hp :

pcellb 0 nx

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

Hlv :

Hi :

icellb 8 z

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" LetTAtom"chk1" A HalfCheckLower 0 8 Read 8 TmpTAtom"chk0"; TmpTAtom"pr.1"; LetTAtom"v15" P RawLoadPointer0 AuxRead; LowerResolve; AddressRead TmpTAtom"chk1" JGotoPollTAtom"L3" {v. Φv}

iApply wp_half_check with Hlv ; first side | iNext ; iIntros Hlv ; gen_env

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e₀ :

listname × word

Hput :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"v12" e₀ = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"v11" e₀ = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v7" e₀ = SomeWIntb

H₁₀ :

lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e₀ = SomeWInt1

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₆ :

lookupTAtom"v13" e₀ = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hp :

pcellb 0 nx

Hl :

lstnx zs

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

Hi :

icellb 8 z

Hlv :

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" LetTAtom"v15" P RawLoadPointer0 AuxRead; LowerResolve; AddressRead TmpTAtom"chk1" JGotoPollTAtom"L3" {v. Φv}

iDestruct lst_cap with Hl as Hnr [Hcap Hl]

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

e₀ :

listname × word

Hput :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"v12" e₀ = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"v11" e₀ = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v7" e₀ = SomeWIntb

H₁₀ :

lookupTAtom"pr.2" e₀ = SomeWIntlist_sumys

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e₀ = SomeWInt1

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₆ :

lookupTAtom"v13" e₀ = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hp :

pcellb 0 nx

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

Hi :

icellb 8 z

Hlv :

Hcap :

live_capptr_capnx node_regptr_addrnx

Hl :

live_capptr_capnx node_regptr_addrnx −∗ lstnx zs

∗

iApply wp_raw_load_pointer with Hlv Hp Hcap ; first side | iNext ; iIntros Hlv Hp Hcap ; iSpecialize Hl with Hcap ; gen_env

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₆ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₄ :

lookupTAtom"v8" e = SomeWInt1

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₃ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₅ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₇ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

Hi :

icellb 8 z

Hl :

lstnx zs

Hlv :

Hp :

pcellb 0 nx

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JGotoPollTAtom"L3" {v. Φv}

wp_goto_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₆ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₄ :

lookupTAtom"v8" e = SomeWInt1

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₁ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₃ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₅ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₇ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

Hi :

icellb 8 z

Hl :

lstnx zs

Hlv :

Hp :

pcellb 0 nx

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"L3" SomeTAtom"L4" {v. Φv}

wp_enter_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

Hi :

icellb 8 z

Hl :

lstnx zs

Hlv :

Hp :

pcellb 0 nx

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" LetTAtom"v7" L Ptoi TmpTAtom"pr.1"; LetTAtom"v8" W CmpNe L TmpTAtom"v7"; Const0 JBranchTmpTAtom"v8" ToTAtom"L4" ToTAtom"L5" {v. Φv}

iApply IH $! _ nx ys ++ z zs with [%] [Hs Hlv Hp Hi] Hl [HΦ]

3 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

⊢

lookupTAtom"pr.1" e = SomeWPtrnx ∧ lookupTAtom"pr.2" e = SomeWIntlist_sumys ++ z

focused goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

∗

lsegp nx ys ++ z

focused goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

lstp ys ++ z ++ zs −∗ ΦRetWIntlist_sumys ++ z ++ zs

+split ; eassumption |

3 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

⊢

lookupTAtom"pr.2" e = SomeWIntlist_sumys ++ z

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

∗

lsegp nx ys ++ z

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

lstp ys ++ z ++ zs −∗ ΦRetWIntlist_sumys ++ z ++ zs

rewrite list_sum_snoc

3 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

⊢

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

∗

lsegp nx ys ++ z

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

lstp ys ++ z ++ zs −∗ ΦRetWIntlist_sumys ++ z ++ zs

eassumption

2 open

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

Hs :

lsegp ptr_addr ≔ b; ptr_cap ≔ Objb ys

Hlv :

Hp :

pcellb 0 nx

Hi :

icellb 8 z

∗

lsegp nx ys ++ z

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

lstp ys ++ z ++ zs −∗ ΦRetWIntlist_sumys ++ z ++ zs

+iApply lseg_snoc with Hs Hlv Hp Hi

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

⊢

node_okptr_addr ≔ b; ptr_cap ≔ Objb b

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

lstp ys ++ z ++ zs −∗ ΦRetWIntlist_sumys ++ z ++ zs

unfold node_ok

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

⊢

ptr_addr ≔ b; ptr_cap ≔ Objb = ptr_addr ≔ b; ptr_cap ≔ Objb ∧ 0 < b ∧ b + 16 ≤ 2 ^ 48 ∧ b mod 16 = 0

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

lstp ys ++ z ++ zs −∗ ΦRetWIntlist_sumys ++ z ++ zs

auto

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

lstp ys ++ z ++ zs −∗ ΦRetWIntlist_sumys ++ z ++ zs

+rewrite - app_assoc

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

Φ :

outcome → iPropIΣ

ys :

listZ

z :

zs :

listZ

b :

H :

0 ≤ list_sumys < 2 ^ 64

nx :

Hb₀ :

0 < b

Hb₁ :

b + 16 ≤ 2 ^ 48

Hb₂ :

b mod 16 = 0

H₀ :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₁ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₂ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₃ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₄ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₅ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₆ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₇ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₈ :

fn_retls_fn"sum" = RClassL

H₉ :

fn_retls_fn"listsum" = RClassL

Hnr :

0 ≤ ptr_addrnx < 2 ^ 64

e :

listname × word

Hput₀ :

lookupTAtom"pr.1" e = SomeWPtrnx

H₁₈ :

lookupTAtom"v15" e = SomeWPtrnx

H₁₆ :

lookupTAtom"v13" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₂ :

lookupTAtom"v8" e = SomeWInt1

H₁₀ :

lookupTAtom"v7" e = SomeWIntb

H₁₁ :

lookupTAtom"v11" e = SomeWPtrptr_addr ≔ b + 8; ptr_cap ≔ Objb

H₁₃ :

lookupTAtom"v12" e = SomeWIntz mod 2 ^ 64

H₁₅ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ b; ptr_cap ≔ Objb

H₁₇ :

lookupTAtom"pr.2" e = SomeWIntlist_sumys + z mod 2 ^ 64 mod 2 ^ 64

IH :

□

HΦ :

lstp ys ++ z :: zs −∗ ΦRetWIntlist_sumys ++ z :: zs

∗

lstp ys ++ z ++ zs −∗ ΦRetWIntlist_sumys ++ z ++ zs

iExact HΦ

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

iLöb as IH

iIntros e q ys zs Hq Hs Hs Hl HΦ

pose proof list_sum_rangeys

destruct zs as | z zs

–iDestruct Hl as %→

cbn [ sum_L3 b_insts b_jump ]

rewrite app_nil_r

iApply wp_ret ; first side | iNext

iApply HΦ

iDestruct lseg_lst_ _ _ [ ] with Hs [//] as H

rewrite app_nil_r

iExact H

–rewrite lst_cons

iDestruct Hl as b nx → & Hb₀ & Hb₁ & Hb₂ (Hlv & Hp & Hi & Hl)

ls_facts

cbn [ sum_L3 b_insts b_jump ]

iApply wp_check with Hlv ; first side | iNext ; iIntros Hlv ; gen_env

iApply wp_raw_load with Hlv Hi ; first side | iNext ; iIntros Hlv Hi ; gen_env

iApply wp_half_check with Hlv ; first side | iNext ; iIntros Hlv ; gen_env

iDestruct lst_cap with Hl as Hnr [Hcap Hl]

iApply wp_raw_load_pointer with Hlv Hp Hcap ; first side | iNext ; iIntros Hlv Hp Hcap ; iSpecialize Hl with Hcap ; gen_env

wp_goto_

iApply IH $! _ nx ys ++ z zs with [%] [Hs Hlv Hp Hi] Hl [HΦ]

+split ; eassumption |

rewrite list_sum_snoc

eassumption

+iApply lseg_snoc with Hs Hlv Hp Hi

unfold node_ok

auto

+rewrite - app_assoc

iExact HΦ

sum's specification: called with the list from p holding xs, it returns their sum modulo 2^64 and hands the list back.

312Lemma sum_spec

∀ p xs

⊢ ⦃lstp xs⦄ ERunsum_framep : lexpr ⦃RET RetWIntlist_sumxs; lstp xs⦄

Explore proof 8 tactics

Initial goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

xs :

listZ

⊢

⊢ ⦃lstp xs⦄ ERunsum_framep : lexpr ⦃RET RetWIntlist_sumxs; lstp xs⦄

iIntros Φ !> Hl HΦ

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

xs :

listZ

Φ :

outcome → iPropIΣ

Hl :

lstp xs

HΦ :

▷lstp xs −∗ ΦRetWIntlist_sumxs

∗

WPERunsum_framep {v. Φv}

ls_facts

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

xs :

listZ

Φ :

outcome → iPropIΣ

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

Hl :

lstp xs

HΦ :

▷lstp xs −∗ ΦRetWIntlist_sumxs

∗

WPERunsum_framep {v. Φv}

unfold sum_frame

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

xs :

listZ

Φ :

outcome → iPropIΣ

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

Hl :

lstp xs

HΦ :

▷lstp xs −∗ ΦRetWIntlist_sumxs

∗

WPERunfr_fn ≔ ls_fn"sum"; fr_env ≔ TAtom"v0", WPtrp; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"start" None {v. Φv}

wp_enter_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

xs :

listZ

Φ :

outcome → iPropIΣ

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

Hl :

lstp xs

HΦ :

lstp xs −∗ ΦRetWIntlist_sumxs

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ TAtom"v0", WPtrp; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"start" [ ] JGotoToTAtom"L3" {v. Φv}

wp_goto_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

xs :

listZ

Φ :

outcome → iPropIΣ

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

Hl :

lstp xs

HΦ :

lstp xs −∗ ΦRetWIntlist_sumxs

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ TAtom"v0", WPtrp; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"L3" SomeTAtom"start" {v. Φv}

wp_enter_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

xs :

listZ

Φ :

outcome → iPropIΣ

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

Hl :

lstp xs

HΦ :

lstp xs −∗ ΦRetWIntlist_sumxs

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ putTAtom"pr.1" WPtrp putTAtom"pr.2" WInt0 TAtom"v0", WPtrp; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L3" LetTAtom"v7" L Ptoi TmpTAtom"pr.1"; LetTAtom"v8" W CmpNe L TmpTAtom"v7"; Const0 JBranchTmpTAtom"v8" ToTAtom"L4" ToTAtom"L5" {v. Φv}

iApply sum_loopp Φ $! _ p [ ] xs with [%] [//] Hl HΦ

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

p :

xs :

listZ

Φ :

outcome → iPropIΣ

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

⊢

lookupTAtom"pr.1" putTAtom"pr.1" WPtrp putTAtom"pr.2" WInt0 TAtom"v0", WPtrp = SomeWPtrp ∧ lookupTAtom"pr.2" putTAtom"pr.1" WPtrp putTAtom"pr.2" WInt0 TAtom"v0", WPtrp = SomeWIntlist_sum[ ]

split ; reflexivity

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

iIntros Φ !> Hl HΦ

unfold sum_frame

iApply sum_loopp Φ $! _ p [ ] xs with [%] [//] Hl HΦ

split ; reflexivity

A new node's object, split into the pieces a node owns: its life, a null next pointer and a zero value; the other aux slots are dropped.

325Lemma obj_node

∀ base

objbase heap_req16 16 −∗ livebase node_regbase ∗ pcellbase 0 null ∗ icellbase 8 0

Explore proof 7 tactics

Initial goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

base :

⊢

objbase heap_req16 16 −∗ livebase node_regbase ∗ pcellbase 0 null ∗ icellbase 8 0

rewrite / obj / live / pcell / icell

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

base :

⊢

ptsobj_psbase heap_req16 16 −∗ ptsPLivebase, VLivenode_regbase ∗ ptsPAuxbase 0, VAuxptr_capnull :: cellbase 0 ptr_addrnull ∗ ptscellbase 8 0

assert E : obj_psbase heap_req16 16 = PLivebase, VLivenode_regbase ++ cellbase 0 0 ++ cellbase 8 0 ++ PAuxbase 0, VAuxCNone ++ λi ⇒ PAuxbase i, VAuxCNone <$> seqZ1 15 by reflexivity

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

base :

E :

obj_psbase heap_req16 16 = PLivebase, VLivenode_regbase ++ cellbase 0 0 ++ cellbase 8 0 ++ PAuxbase 0, VAuxCNone ++ λi : Z ⇒ PAuxbase i, VAuxCNone <$> seqZ1 15

⊢

ptsobj_psbase heap_req16 16 −∗ ptsPLivebase, VLivenode_regbase ∗ ptsPAuxbase 0, VAuxptr_capnull :: cellbase 0 ptr_addrnull ∗ ptscellbase 8 0

rewrite E ! pts_app

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

base :

E :

obj_psbase heap_req16 16 = PLivebase, VLivenode_regbase ++ cellbase 0 0 ++ cellbase 8 0 ++ PAuxbase 0, VAuxCNone ++ λi : Z ⇒ PAuxbase i, VAuxCNone <$> seqZ1 15

⊢

ptsPLivebase, VLivenode_regbase ∗ ptscellbase 0 0 ∗ ptscellbase 8 0 ∗ ptsPAuxbase 0, VAuxCNone ∗ ptsλi : Z ⇒ PAuxbase i, VAuxCNone <$> seqZ1 15 −∗ ptsPLivebase, VLivenode_regbase ∗ ptsPAuxbase 0, VAuxptr_capnull :: cellbase 0 ptr_addrnull ∗ ptscellbase 8 0

iIntros (Hl & H₀ & H₈ & Ha & _)

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

base :

E :

obj_psbase heap_req16 16 = PLivebase, VLivenode_regbase ++ cellbase 0 0 ++ cellbase 8 0 ++ PAuxbase 0, VAuxCNone ++ λi : Z ⇒ PAuxbase i, VAuxCNone <$> seqZ1 15

Hl :

ptsPLivebase, VLivenode_regbase

H₀ :

ptscellbase 0 0

H₈ :

ptscellbase 8 0

Ha :

ptsPAuxbase 0, VAuxCNone

∗

ptsPLivebase, VLivenode_regbase ∗ ptsPAuxbase 0, VAuxptr_capnull :: cellbase 0 ptr_addrnull ∗ ptscellbase 8 0

iFrame Hl H₈

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

base :

E :

obj_psbase heap_req16 16 = PLivebase, VLivenode_regbase ++ cellbase 0 0 ++ cellbase 8 0 ++ PAuxbase 0, VAuxCNone ++ λi : Z ⇒ PAuxbase i, VAuxCNone <$> seqZ1 15

H₀ :

ptscellbase 0 0

Ha :

ptsPAuxbase 0, VAuxCNone

∗

ptsPAuxbase 0, VAuxptr_capnull :: cellbase 0 ptr_addrnull

rewrite pts_app_ cellbase 0 0

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

base :

E :

obj_psbase heap_req16 16 = PLivebase, VLivenode_regbase ++ cellbase 0 0 ++ cellbase 8 0 ++ PAuxbase 0, VAuxCNone ++ λi : Z ⇒ PAuxbase i, VAuxCNone <$> seqZ1 15

H₀ :

ptscellbase 0 0

Ha :

ptsPAuxbase 0, VAuxCNone

∗

ptsPAuxbase 0, VAuxptr_capnull ∗ ptscellbase 0 0

iFrame

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

rewrite / obj / live / pcell / icell

assert E : obj_psbase heap_req16 16 = PLivebase, VLivenode_regbase ++ cellbase 0 0 ++ cellbase 8 0 ++ PAuxbase 0, VAuxCNone ++ λi ⇒ PAuxbase i, VAuxCNone <$> seqZ1 15 by reflexivity

rewrite E ! pts_app

iIntros (Hl & H₀ & H₈ & Ha & _)

iFrame Hl H₈

rewrite pts_app_ cellbase 0 0

iFrame

listsum's loop, from the point after its head's phis: with pr.2 an int i in range, pr.1 the list's pointer h and v0 the input n, owning the list, the run is safe. By Löb induction; each iteration allocates a node, stores h and i in it, and the loop goes on with i + 1 and the longer list; at the end sum is called with the list through its triple, and the list it hands back is dropped.

343Lemma ls_loop

∀ n

⊢ ∀e i h xs, ⌜lookupTAtom"pr.2" e = SomeWInti ∧ 0 ≤ i < 2 ^ 31 ∧ lookupTAtom"pr.1" e = SomeWPtrh ∧ lookupTAtom"v0" e = SomeWIntn⌝ −∗ lsth xs −∗ WPERunmkFramels_fn"listsum" e [ ] None ExecTAtom"L4" b_instsls_L4 b_jumpls_L4 : lexpr {_. True}

Explore proof 49 tactics

Initial goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

⊢

⊢ ∀e : listname × word i : Z h : ptr xs : listZ, ⌜lookupTAtom"pr.2" e = SomeWInti ∧ 0 ≤ i < 2 ^ 31 ∧ lookupTAtom"pr.1" e = SomeWPtrh ∧ lookupTAtom"v0" e = SomeWIntn⌝ −∗ lsth xs −∗ WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" b_instsls_L4 b_jumpls_L4 : lexpr {_. True}

iLöb as IH

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

IH :

▷∀e : listname × word i : Z h : ptr xs : listZ, ⌜lookupTAtom"pr.2" e = SomeWInti ∧ 0 ≤ i < 2 ^ 31 ∧ lookupTAtom"pr.1" e = SomeWPtrh ∧ lookupTAtom"v0" e = SomeWIntn⌝ −∗ lsth xs −∗ WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" b_instsls_L4 b_jumpls_L4 {_. True}

□

∀e : listname × word i : Z h : ptr xs : listZ, ⌜lookupTAtom"pr.2" e = SomeWInti ∧ 0 ≤ i < 2 ^ 31 ∧ lookupTAtom"pr.1" e = SomeWPtrh ∧ lookupTAtom"v0" e = SomeWIntn⌝ −∗ lsth xs −∗ WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" b_instsls_L4 b_jumpls_L4 {_. True}

iIntros e i h xs Hi & Hir & Hh & Hn Hl

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

e :

listname × word

i :

h :

xs :

listZ

Hi :

lookupTAtom"pr.2" e = SomeWInti

Hir :

0 ≤ i < 2 ^ 31

Hh :

lookupTAtom"pr.1" e = SomeWPtrh

Hn :

lookupTAtom"v0" e = SomeWIntn

IH :

▷∀e₀ : listname × word i₀ : Z h₀ : ptr xs₀ : listZ, ⌜lookupTAtom"pr.2" e₀ = SomeWInti₀ ∧ 0 ≤ i₀ < 2 ^ 31 ∧ lookupTAtom"pr.1" e₀ = SomeWPtrh₀ ∧ lookupTAtom"v0" e₀ = SomeWIntn⌝ −∗ lsth₀ xs₀ −∗ WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" b_instsls_L4 b_jumpls_L4 {_. True}

□

Hl :

lsth xs

∗

WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" b_instsls_L4 b_jumpls_L4 {_. True}

ls_facts

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

e :

listname × word

i :

h :

xs :

listZ

Hi :

lookupTAtom"pr.2" e = SomeWInti

Hir :

0 ≤ i < 2 ^ 31

Hh :

lookupTAtom"pr.1" e = SomeWPtrh

Hn :

lookupTAtom"v0" e = SomeWIntn

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

IH :

□

Hl :

lsth xs

∗

WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" b_instsls_L4 b_jumpls_L4 {_. True}

pose proof ls_find_sumR.free

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

e :

listname × word

i :

h :

xs :

listZ

Hi :

lookupTAtom"pr.2" e = SomeWInti

Hir :

0 ≤ i < 2 ^ 31

Hh :

lookupTAtom"pr.1" e = SomeWPtrh

Hn :

lookupTAtom"v0" e = SomeWIntn

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

IH :

□

Hl :

lsth xs

∗

WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" b_instsls_L4 b_jumpls_L4 {_. True}

cbn [ ls_L4 b_insts b_jump ]

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

e :

listname × word

i :

h :

xs :

listZ

Hi :

lookupTAtom"pr.2" e = SomeWInti

Hir :

0 ≤ i < 2 ^ 31

Hh :

lookupTAtom"pr.1" e = SomeWPtrh

Hn :

lookupTAtom"v0" e = SomeWIntn

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

IH :

□

Hl :

lsth xs

∗

WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" LetTAtom"v10" W CmpSlt W TmpTAtom"pr.2"; TmpTAtom"v0" JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

wp_let_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hput :

lookupTAtom"v10" e₀

Some

WInt

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

→

else

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

∀e : listname × word i₀ : Z h₀ : ptr xs₀ : listZ, ⌜lookupTAtom"pr.2" e = SomeWInti₀ ∧ 0 ≤ i₀ < 2 ^ 31 ∧ lookupTAtom"pr.1" e = SomeWPtrh₀ ∧ lookupTAtom"v0" e = SomeWIntn⌝ −∗ lsth₀ xs₀ −∗ WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" LetTAtom"v10" W CmpSlt W TmpTAtom"pr.2"; TmpTAtom"v0" JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

match goal withH : lookupTAtom"v10" _ = SomeWIntif ?c then 1 else 0 |- _⇒destruct c eqn: Hcend

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hput :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

focused goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

–assert Hi₁ : i + 1 < 2 ^ 31

3 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hput :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

⊢

i + 1 < 2 ^ 31

focused goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hput :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

Hi₁ :

i + 1 < 2 ^ 31

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

{apply Z.ltb_lt in Hc

3 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

Hput :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

⊢

i + 1 < 2 ^ 31

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hput :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

Hi₁ :

i + 1 < 2 ^ 31

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

revert Hc

3 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hput :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

⊢

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

→

i + 1 < 2 ^ 31

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hput :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

Hi₁ :

i + 1 < 2 ^ 31

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

destruct 2 ^ 31 ≤? n mod 2 ^ 32 eqn: Hs ; apply Z.leb_le in Hs | apply Z.leb_gt in Hs ; intros ; pose proof Z.mod_pos_boundn 2 ^ 32 ltac:lia ; lia

2 open

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hput :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

Hi₁ :

i + 1 < 2 ^ 31

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

wp_branch_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hput :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

Hi₁ :

i + 1 < 2 ^ 31

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"L5" SomeTAtom"L4" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

wp_enter_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hput :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

Hi₁ :

i + 1 < 2 ^ 31

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L5" LetTAtom"v12" P Alloc16 Const16; LetTAtom"chk0" A Check0 8 Write 8 TmpTAtom"v12"; RawStorePointer0 TmpTAtom"pr.1" TmpTAtom"chk0" AuxEnsure; LowerBarrier; RootedReload; LowerWrite; AddressWrite; FlightTAtom"v16" Add FAddressTmpTAtom"v12"; FValueConst8 LowerOfTmpTAtom"v12"; LetTAtom"v18" L ExtSw TmpTAtom"pr.2"; LetTAtom"chk1" A HalfCheckUpper 0 8 Write 1 TmpTAtom"chk0"; TmpTAtom"v16"; RawStoreWl 0 TmpTAtom"v18" TmpTAtom"chk1"; LetTAtom"v21" W Add TmpTAtom"pr.2"; Const1 JGotoPollTAtom"L4" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iApply wp_alloc ; first side | iNext ; iIntros base Hb₀ & Hb₁ & Hb₂ Hobj ; gen_env

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod req_alignheap_req16 16 = 0

Hb₂ :

base + req_extentheap_req16 16 ≤ 2 ^ 48

e :

listname × word

Hput₀ :

lookupTAtom"v12" e = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"pr.2" e = SomeWInti

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrh

H₁₁ :

lookupTAtom"v0" e = SomeWIntn

H₁₀ :

lookupTAtom"v10" e = SomeWInt1

IH :

∀e₀ : listname × word i₀ : Z h₀ : ptr xs₀ : listZ, ⌜lookupTAtom"pr.2" e₀ = SomeWInti₀ ∧ 0 ≤ i₀ < 2 ^ 31 ∧ lookupTAtom"pr.1" e₀ = SomeWPtrh₀ ∧ lookupTAtom"v0" e₀ = SomeWIntn⌝ −∗ lsth₀ xs₀ −∗ WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" LetTAtom"v10" W CmpSlt W TmpTAtom"pr.2"; TmpTAtom"v0" JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

□

Hl :

lsth xs

Hobj :

objbase heap_req16 16

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L5" LetTAtom"chk0" A Check0 8 Write 8 TmpTAtom"v12"; RawStorePointer0 TmpTAtom"pr.1" TmpTAtom"chk0" AuxEnsure; LowerBarrier; RootedReload; LowerWrite; AddressWrite; FlightTAtom"v16" Add FAddressTmpTAtom"v12"; FValueConst8 LowerOfTmpTAtom"v12"; LetTAtom"v18" L ExtSw TmpTAtom"pr.2"; LetTAtom"chk1" A HalfCheckUpper 0 8 Write 1 TmpTAtom"chk0"; TmpTAtom"v16"; RawStoreWl 0 TmpTAtom"v18" TmpTAtom"chk1"; LetTAtom"v21" W Add TmpTAtom"pr.2"; Const1 JGotoPollTAtom"L4" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

change req_alignheap_req16 16 with 16 in Hb₁

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + req_extentheap_req16 16 ≤ 2 ^ 48

e :

listname × word

Hput₀ :

lookupTAtom"v12" e = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"pr.2" e = SomeWInti

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrh

H₁₁ :

lookupTAtom"v0" e = SomeWIntn

H₁₀ :

lookupTAtom"v10" e = SomeWInt1

IH :

□

Hl :

lsth xs

Hobj :

objbase heap_req16 16

∗

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

change req_extentheap_req16 16 with 16 in Hb₂

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e :

listname × word

Hput₀ :

lookupTAtom"v12" e = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"pr.2" e = SomeWInti

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrh

H₁₁ :

lookupTAtom"v0" e = SomeWIntn

H₁₀ :

lookupTAtom"v10" e = SomeWInt1

IH :

□

Hl :

lsth xs

Hobj :

objbase heap_req16 16

∗

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iDestruct obj_node with Hobj as (Hlv & Hp & Hi)

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e :

listname × word

Hput₀ :

lookupTAtom"v12" e = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"pr.2" e = SomeWInti

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrh

H₁₁ :

lookupTAtom"v0" e = SomeWIntn

H₁₀ :

lookupTAtom"v10" e = SomeWInt1

IH :

□

Hl :

lsth xs

Hlv :

livebase node_regbase

Hp :

pcellbase 0 null

Hi :

icellbase 8 0

∗

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iApply wp_check with Hlv ; first side | iNext ; iIntros Hlv ; gen_env

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₄ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

H₁₃ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

IH :

□

Hl :

lsth xs

Hp :

pcellbase 0 null

Hi :

icellbase 8 0

Hlv :

livebase node_regbase

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L5" RawStorePointer0 TmpTAtom"pr.1" TmpTAtom"chk0" AuxEnsure; LowerBarrier; RootedReload; LowerWrite; AddressWrite; FlightTAtom"v16" Add FAddressTmpTAtom"v12"; FValueConst8 LowerOfTmpTAtom"v12"; LetTAtom"v18" L ExtSw TmpTAtom"pr.2"; LetTAtom"chk1" A HalfCheckUpper 0 8 Write 1 TmpTAtom"chk0"; TmpTAtom"v16"; RawStoreWl 0 TmpTAtom"v18" TmpTAtom"chk1"; LetTAtom"v21" W Add TmpTAtom"pr.2"; Const1 JGotoPollTAtom"L4" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iApply wp_raw_store_pointer with Hlv Hp ; first side | iNext ; iIntros Hlv Hp ; gen_env

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₄ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

H₁₃ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

IH :

□

Hl :

lsth xs

Hi :

icellbase 8 0

Hlv :

livebase node_regbase

Hp :

pcellbase 0 h

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L5" FlightTAtom"v16" Add FAddressTmpTAtom"v12"; FValueConst8 LowerOfTmpTAtom"v12"; LetTAtom"v18" L ExtSw TmpTAtom"pr.2"; LetTAtom"chk1" A HalfCheckUpper 0 8 Write 1 TmpTAtom"chk0"; TmpTAtom"v16"; RawStoreWl 0 TmpTAtom"v18" TmpTAtom"chk1"; LetTAtom"v21" W Add TmpTAtom"pr.2"; Const1 JGotoPollTAtom"L4" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

wp_flight_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e :

listname × word

Hput₀ :

lookupTAtom"v16" e = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"v12" e = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"pr.2" e = SomeWInti

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrh

H₁₁ :

lookupTAtom"v0" e = SomeWIntn

H₁₀ :

lookupTAtom"v10" e = SomeWInt1

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

IH :

□

Hl :

lsth xs

Hi :

icellbase 8 0

Hlv :

livebase node_regbase

Hp :

pcellbase 0 h

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L5" LetTAtom"v18" L ExtSw TmpTAtom"pr.2"; LetTAtom"chk1" A HalfCheckUpper 0 8 Write 1 TmpTAtom"chk0"; TmpTAtom"v16"; RawStoreWl 0 TmpTAtom"v18" TmpTAtom"chk1"; LetTAtom"v21" W Add TmpTAtom"pr.2"; Const1 JGotoPollTAtom"L4" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

wp_let_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"v18" e₀ = SomeWInti

H₁₆ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₄ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

H₁₃ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

IH :

□

Hl :

lsth xs

Hi :

icellbase 8 0

Hlv :

livebase node_regbase

Hp :

pcellbase 0 h

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L5" LetTAtom"chk1" A HalfCheckUpper 0 8 Write 1 TmpTAtom"chk0"; TmpTAtom"v16"; RawStoreWl 0 TmpTAtom"v18" TmpTAtom"chk1"; LetTAtom"v21" W Add TmpTAtom"pr.2"; Const1 JGotoPollTAtom"L4" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iApply wp_half_check with Hlv ; first side | iNext ; iIntros Hlv ; gen_env

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e :

listname × word

Hput₀ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"v16" e = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"v12" e = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"pr.2" e = SomeWInti

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrh

H₁₁ :

lookupTAtom"v0" e = SomeWIntn

H₁₀ :

lookupTAtom"v10" e = SomeWInt1

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₆ :

lookupTAtom"v18" e = SomeWInti

IH :

□

Hl :

lsth xs

Hi :

icellbase 8 0

Hp :

pcellbase 0 h

Hlv :

livebase node_regbase

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L5" RawStoreWl 0 TmpTAtom"v18" TmpTAtom"chk1"; LetTAtom"v21" W Add TmpTAtom"pr.2"; Const1 JGotoPollTAtom"L4" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iApply wp_raw_store with Hlv Hi ; first side | iNext ; iIntros Hlv Hi ; gen_env

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e :

listname × word

Hput₀ :

lookupTAtom"chk1" e = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"v16" e = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"v12" e = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"pr.2" e = SomeWInti

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrh

H₁₁ :

lookupTAtom"v0" e = SomeWIntn

H₁₀ :

lookupTAtom"v10" e = SomeWInt1

H₁₄ :

lookupTAtom"chk0" e = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₆ :

lookupTAtom"v18" e = SomeWInti

IH :

□

Hl :

lsth xs

Hp :

pcellbase 0 h

Hlv :

livebase node_regbase

Hi :

icellbase 8 i

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L5" LetTAtom"v21" W Add TmpTAtom"pr.2"; Const1 JGotoPollTAtom"L4" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

wp_let_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₈ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₆ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₄ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

H₁₃ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

IH :

□

Hl :

lsth xs

Hp :

pcellbase 0 h

Hlv :

livebase node_regbase

Hi :

icellbase 8 i

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L5" [ ] JGotoPollTAtom"L4" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

wp_goto_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₈ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₆ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₄ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

H₁₃ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

IH :

□

Hl :

lsth xs

Hp :

pcellbase 0 h

Hlv :

livebase node_regbase

Hi :

icellbase 8 i

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"L4" SomeTAtom"L5" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

wp_enter_

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

IH :

□

Hl :

lsth xs

Hp :

pcellbase 0 h

Hlv :

livebase node_regbase

Hi :

icellbase 8 i

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" LetTAtom"v10" W CmpSlt W TmpTAtom"pr.2"; TmpTAtom"v0" JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iApply IH $! _ i + 1 mkPtrbase Objbase i :: xs with [%] [Hlv Hp Hi Hl]

3 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

⊢

lookupTAtom"pr.2" e₀ = SomeWInti + 1 ∧ 0 ≤ i + 1 < 2 ^ 31 ∧ lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase ∧ lookupTAtom"v0" e₀ = SomeWIntn

focused goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

IH :

□

Hlv :

livebase node_regbase

Hp :

pcellbase 0 h

Hi :

icellbase 8 i

Hl :

lsth xs

∗

lstptr_addr ≔ base; ptr_cap ≔ Objbase i :: xs

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

+split ; eassumption |

3 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

⊢

0 ≤ i + 1 < 2 ^ 31 ∧ lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase ∧ lookupTAtom"v0" e₀ = SomeWIntn

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

IH :

□

Hlv :

livebase node_regbase

Hp :

pcellbase 0 h

Hi :

icellbase 8 i

Hl :

lsth xs

∗

lstptr_addr ≔ base; ptr_cap ≔ Objbase i :: xs

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

split ; lia |

3 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

⊢

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase ∧ lookupTAtom"v0" e₀ = SomeWIntn

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

IH :

□

Hlv :

livebase node_regbase

Hp :

pcellbase 0 h

Hi :

icellbase 8 i

Hl :

lsth xs

∗

lstptr_addr ≔ base; ptr_cap ≔ Objbase i :: xs

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

split ; eassumption

2 open

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

IH :

□

Hlv :

livebase node_regbase

Hp :

pcellbase 0 h

Hi :

icellbase 8 i

Hl :

lsth xs

∗

lstptr_addr ≔ base; ptr_cap ≔ Objbase i :: xs

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

+rewrite lst_cons

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

IH :

□

Hlv :

livebase node_regbase

Hp :

pcellbase 0 h

Hi :

icellbase 8 i

Hl :

lsth xs

∗

∃b : Z nx : ptr, ⌜node_okptr_addr ≔ base; ptr_cap ≔ Objbase b⌝ ∗ liveb node_regb ∗ pcellb 0 nx ∗ icellb 8 i ∗ lstnx xs

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iExists base, h

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

IH :

□

Hlv :

livebase node_regbase

Hp :

pcellbase 0 h

Hi :

icellbase 8 i

Hl :

lsth xs

∗

⌜node_okptr_addr ≔ base; ptr_cap ≔ Objbase base⌝ ∗ livebase node_regbase ∗ pcellbase 0 h ∗ icellbase 8 i ∗ lsth xs

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iFrame

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

IH :

□

⌜node_okptr_addr ≔ base; ptr_cap ≔ Objbase base⌝

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iPureIntro

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

⊢

node_okptr_addr ≔ base; ptr_cap ≔ Objbase base

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

unfold node_ok

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

true

Hi₁ :

i + 1 < 2 ^ 31

base :

Hb₀ :

0 < base

Hb₁ :

base mod 16 = 0

Hb₂ :

base + 16 ≤ 2 ^ 48

e₀ :

listname × word

Hput :

lookupTAtom"pr.1" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₈ :

lookupTAtom"v21" e₀ = SomeWInti + 1

H₁₆ :

lookupTAtom"v18" e₀ = SomeWInti

H₁₄ :

lookupTAtom"chk0" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₃ :

lookupTAtom"v10" e₀ = SomeWInt1

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"v12" e₀ = SomeWPtrptr_addr ≔ base; ptr_cap ≔ Objbase

H₁₂ :

lookupTAtom"v16" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₅ :

lookupTAtom"chk1" e₀ = SomeWPtrptr_addr ≔ base + 8; ptr_cap ≔ Objbase

H₁₇ :

lookupTAtom"pr.2" e₀ = SomeWInti + 1

⊢

ptr_addr ≔ base; ptr_cap ≔ Objbase = ptr_addr ≔ base; ptr_cap ≔ Objbase ∧ 0 < base ∧ base + 16 ≤ 2 ^ 48 ∧ base mod 16 = 0

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

auto with zarith

deferred goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" [ ] JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

–wp_branch_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"L7" SomeTAtom"L4" {_. True}

wp_enter_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" CallCResultTAtom"v23" L GlobalTAtom"sum" ArgP TmpTAtom"pr.1" JRetTmpTAtom"v23" {_. True}

iApply wp_call_bind ; try side

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

▷WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ TAtom"v0", WPtrh; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"start" None {o. ∃cf′ : frame, ⌜L.resumefr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23" pd_res ≔ CResultTAtom"v23" L; pd_conv ≔ None o = Somecf′⌝ ∗ ▷WPL.ERuncf′ {_. True}}

iNext

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

Hl :

lsth xs

∗

WPL.ERunfr_fn ≔ ls_fn"sum"; fr_env ≔ TAtom"v0", WPtrh; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"start" None {o. ∃cf′ : frame, ⌜L.resumefr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23" pd_res ≔ CResultTAtom"v23" L; pd_conv ≔ None o = Somecf′⌝ ∗ ▷WPL.ERuncf′ {_. True}}

iApply sum_spec with Hl

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

▷lsth xs −∗ ∃cf′ : frame, ⌜L.resumefr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23" pd_res ≔ CResultTAtom"v23" L; pd_conv ≔ None RetWIntlist_sumxs = Somecf′⌝ ∗ ▷WPL.ERuncf′ {_. True}

iNext

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

lsth xs −∗ ∃cf′ : frame, ⌜L.resumefr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23" pd_res ≔ CResultTAtom"v23" L; pd_conv ≔ None RetWIntlist_sumxs = Somecf′⌝ ∗ ▷WPL.ERuncf′ {_. True}

iIntros _

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

∃cf′ : frame, ⌜L.resumefr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23" pd_res ≔ CResultTAtom"v23" L; pd_conv ≔ None RetWIntlist_sumxs = Somecf′⌝ ∗ ▷WPL.ERuncf′ {_. True}

iExists _

2 open

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

⌜L.resumefr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23" pd_res ≔ CResultTAtom"v23" L; pd_conv ≔ None RetWIntlist_sumxs = Some?f⌝ ∗ ▷WPL.ERun?f {_. True}

shelved goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

⊢

frame

iSplit ; iPureIntro ; reflexivity |

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

▷WPL.ERunfr_fn ≔ fr_fnfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23"; fr_env ≔ putTAtom"v23" WIntlist_sumxs mod 2 ^ 64 fr_envfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23"; fr_locals ≔ fr_localsfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23"; fr_doomed ≔ fr_doomedfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23"; fr_at ≔ fr_atfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23" {_. True}

iNext

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

WPL.ERunfr_fn ≔ fr_fnfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23"; fr_env ≔ putTAtom"v23" WIntlist_sumxs mod 2 ^ 64 fr_envfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23"; fr_locals ≔ fr_localsfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23"; fr_doomed ≔ fr_doomedfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23"; fr_at ≔ fr_atfr_fn ≔ ls_fn"listsum"; fr_env ≔ e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23" {_. True}

cbn [ fr_fn fr_env fr_locals fr_doomed fr_at ]

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

e₀ :

listname × word

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

Hput :

lookupTAtom"v10" e₀ = SomeWInt0

H₁₀ :

lookupTAtom"v0" e₀ = SomeWIntn

H₁₁ :

lookupTAtom"pr.1" e₀ = SomeWPtrh

H₁₂ :

lookupTAtom"pr.2" e₀ = SomeWInti

IH :

□

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ putTAtom"v23" WIntlist_sumxs mod 2 ^ 64 e₀; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23" {_. True}

gen_env

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n, i :

h :

xs :

listZ

Hir :

0 ≤ i < 2 ^ 31

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

H₉ :

find_fnls_geR.free TAtom"sum" = SomeDefinedls_fn"sum"

Hc :

2 ^ 31 ≤? n mod 2 ^ 32

→

n mod 2 ^ 32 − 2 ^ 32

else

n mod 2 ^ 32

false

e :

listname × word

Hput₀ :

lookupTAtom"v23" e = SomeWIntlist_sumxs mod 2 ^ 64

H₁₃ :

lookupTAtom"pr.2" e = SomeWInti

H₁₂ :

lookupTAtom"pr.1" e = SomeWPtrh

H₁₁ :

lookupTAtom"v0" e = SomeWIntn

H₁₀ :

lookupTAtom"v10" e = SomeWInt0

IH :

□

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ e; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L7" [ ] JRetTmpTAtom"v23" {_. True}

iApply wp_ret ; first side | done

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

iLöb as IH

iIntros e i h xs Hi & Hir & Hh & Hn Hl

ls_facts

pose proof ls_find_sumR.free

cbn [ ls_L4 b_insts b_jump ]

match goal withH : lookupTAtom"v10" _ = SomeWIntif ?c then 1 else 0 |- _⇒destruct c eqn: Hcend

–assert Hi₁ : i + 1 < 2 ^ 31

{apply Z.ltb_lt in Hc

revert Hc

destruct 2 ^ 31 ≤? n mod 2 ^ 32 eqn: Hs ; apply Z.leb_le in Hs | apply Z.leb_gt in Hs ; intros ; pose proof Z.mod_pos_boundn 2 ^ 32 ltac:lia ; lia

wp_branch_

iApply wp_alloc ; first side | iNext ; iIntros base Hb₀ & Hb₁ & Hb₂ Hobj ; gen_env

change req_alignheap_req16 16 with 16 in Hb₁

change req_extentheap_req16 16 with 16 in Hb₂

iDestruct obj_node with Hobj as (Hlv & Hp & Hi)

iApply wp_check with Hlv ; first side | iNext ; iIntros Hlv ; gen_env

iApply wp_raw_store_pointer with Hlv Hp ; first side | iNext ; iIntros Hlv Hp ; gen_env

wp_flight_

iApply wp_half_check with Hlv ; first side | iNext ; iIntros Hlv ; gen_env

iApply wp_raw_store with Hlv Hi ; first side | iNext ; iIntros Hlv Hi ; gen_env

wp_goto_

iApply IH $! _ i + 1 mkPtrbase Objbase i :: xs with [%] [Hlv Hp Hi Hl]

+split ; eassumption |

split ; lia |

split ; eassumption

+rewrite lst_cons

iExists base, h

iFrame

iPureIntro

unfold node_ok

auto with zarith

–wp_branch_

iApply wp_call_bind ; try side

iNext

iApply sum_spec with Hl

iNext

iIntros _

iExists _

iSplit ; iPureIntro ; reflexivity |

iNext

cbn [ fr_fn fr_env fr_locals fr_doomed fr_at ]

gen_env

iApply wp_ret ; first side | done

listsum called with the int n is safe.

383Lemma listsum_spec

∀ n

⊢ WPERunmkFramels_fn"listsum" TAtom"v0", WIntn [ ] None EnterTAtom"start" None : lexpr {_. True}

Explore proof 8 tactics

Initial goal

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

⊢

⊢ WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ TAtom"v0", WIntn; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"start" None : lexpr {_. True}

ls_facts

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

⊢

⊢ WPERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ TAtom"v0", WIntn; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"start" None : lexpr {_. True}

wp_enter_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ TAtom"v0", WIntn; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"start" [ ] JGotoToTAtom"L4" {_. True}

wp_goto_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ TAtom"v0", WIntn; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ EnterTAtom"L4" SomeTAtom"start" {_. True}

wp_enter_

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

∗

WPL.ERunfr_fn ≔ ls_fn"listsum"; fr_env ≔ putTAtom"pr.1" WPtrptr_addr ≔ 0; ptr_cap ≔ CNone putTAtom"pr.2" WInt0 TAtom"v0", WIntn; fr_locals ≔ [ ]; fr_doomed ≔ None; fr_at ≔ ExecTAtom"L4" LetTAtom"v10" W CmpSlt W TmpTAtom"pr.2"; TmpTAtom"v0" JBranchTmpTAtom"v10" ToTAtom"L5" ToTAtom"L7" {_. True}

iApply ls_loopn $! _ 0 null [ ] with [%] [//]

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

⊢

lookupTAtom"pr.2" putTAtom"pr.1" WPtrptr_addr ≔ 0; ptr_cap ≔ CNone putTAtom"pr.2" WInt0 TAtom"v0", WIntn = SomeWInt0 ∧ 0 ≤ 0 < 2 ^ 31 ∧ lookupTAtom"pr.1" putTAtom"pr.1" WPtrptr_addr ≔ 0; ptr_cap ≔ CNone putTAtom"pr.2" WInt0 TAtom"v0", WIntn = SomeWPtrnull ∧ lookupTAtom"v0" putTAtom"pr.1" WPtrptr_addr ≔ 0; ptr_cap ≔ CNone putTAtom"pr.2" WInt0 TAtom"v0", WIntn = SomeWIntn

split ; reflexivity |

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

⊢

0 ≤ 0 < 2 ^ 31 ∧ lookupTAtom"pr.1" putTAtom"pr.1" WPtrptr_addr ≔ 0; ptr_cap ≔ CNone putTAtom"pr.2" WInt0 TAtom"v0", WIntn = SomeWPtrnull ∧ lookupTAtom"v0" putTAtom"pr.1" WPtrptr_addr ≔ 0; ptr_cap ≔ CNone putTAtom"pr.2" WInt0 TAtom"v0", WIntn = SomeWIntn

split ; lia |

hlc :

has_lc

Σ :

gFunctors

invGS_gen₀ :

invGS_genhlc Σ

gen_heapGS₀ :

gen_heapGSpiece pval Σ

n :

H :

find_blockTAtom"start" fn_blocksls_fn"sum" = Somesum_start

H₀ :

find_blockTAtom"L3" fn_blocksls_fn"sum" = Somesum_L3

H₁ :

find_blockTAtom"L4" fn_blocksls_fn"sum" = Somesum_L4

H₂ :

find_blockTAtom"L5" fn_blocksls_fn"sum" = Somesum_L5

H₃ :

find_blockTAtom"start" fn_blocksls_fn"listsum" = Somels_start

H₄ :

find_blockTAtom"L4" fn_blocksls_fn"listsum" = Somels_L4

H₅ :

find_blockTAtom"L5" fn_blocksls_fn"listsum" = Somels_L5

H₆ :

find_blockTAtom"L7" fn_blocksls_fn"listsum" = Somels_L7

H₇ :

fn_retls_fn"sum" = RClassL

H₈ :

fn_retls_fn"listsum" = RClassL

⊢

lookupTAtom"pr.1" putTAtom"pr.1" WPtrptr_addr ≔ 0; ptr_cap ≔ CNone putTAtom"pr.2" WInt0 TAtom"v0", WIntn = SomeWPtrnull ∧ lookupTAtom"v0" putTAtom"pr.1" WPtrptr_addr ≔ 0; ptr_cap ≔ CNone putTAtom"pr.2" WInt0 TAtom"v0", WIntn = SomeWIntn

split ; reflexivity

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

iApply ls_loopn $! _ 0 null [ ] with [%] [//]

split ; reflexivity |

split ; lia |

split ; reflexivity

The resources the proof uses: invariants and the ghost heap.

395Definition lsΣ: gFunctors ≔

#invΣ; gen_heapΣpiece pval

lsΣ has invariants.

398Instance lsΣ_inv: invGpreSlsΣ

Explore proof 2 tactics

Initial goal

⊢

invGpreSlsΣ

apply subG_invΣ

⊢

subGinvΣ lsΣ

apply _

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

apply subG_invΣ

apply _

lsΣ has the ghost heap of pieces.

402Instance lsΣ_heap: gen_heapGpreSpiece pval lsΣ

Explore proof 2 tactics

Initial goal

⊢

gen_heapGpreSpiece pval lsΣ

apply subG_gen_heapGpreS

⊢

subGgen_heapΣpiece pval lsΣ

apply _

No remaining goals.

Qed

✓ Proof checked and closed by Rocq.

Source script

apply subG_gen_heapGpreS

apply _

listsum never panics: for every input whose first word is an int, with any fuel, no state of its run fails, whatever bases its nodes get. Proved by Iris adequacy (heap_never_panics) from listsum_spec.

409Theorem listsum_never_panics

P.never_panicsls_module TAtom"listsum" λxs ⇒ ∃n rest, xs = WIntn :: rest

Explore proof 11 tactics

Initial goal

⊢

P.never_panicsls_module TAtom"listsum" λxs : listword ⇒ ∃n : Z rest : listword, xs = WIntn :: rest

apply heap_never_panicslsΣ ls_module TAtom"listsum" _ ls_globals ListSum.ls_mem ls_fn"listsum"

4 open

⊢

initial_memoryls_module = Somels_globals, ListSum.ls_mem

focused goal

⊢

find_fnlge TAtom"listsum" = SomeDefinedls_fn"listsum"

focused goal

⊢

live_disjointListSum.ls_mem

focused goal

⊢

∀xs : listword, ∃n : Z rest : listword, xs = WIntn :: rest → ∃fr : frame, call_framels_fn"listsum" xs = Somefr ∧ ∀HinvG : invGS_genHasNoLc lsΣ HheapG : gen_heapGSpiece pval lsΣ, ⊢ WPL.ERunfr {_. True}

–exact ls_initial

3 open

deferred goal

⊢

find_fnlge TAtom"listsum" = SomeDefinedls_fn"listsum"

deferred goal

⊢

live_disjointListSum.ls_mem

deferred goal

⊢

–exact ls_find_listsumR.free

2 open

deferred goal

⊢

live_disjointListSum.ls_mem

deferred goal

⊢

–intros b₁ r₁ b₂ r₂ E _

2 open

b₁ :

r₁ :

b₂ :

r₂ :

E :

object_regionb₁ m_regionsListSum.ls_mem = Somer₁

⊢

live_atListSum.ls_mem b₂ r₂ → b₁ ≠ b₂ → r_endr₁ ≤ b₂ ∨ r_endr₂ ≤ b₁

deferred goal

⊢

vm_compute in E

2 open

b₁ :

r₁ :

b₂ :

r₂ :