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Proof step 86 from proof fsync-pages-others-unchanged (previous step)

# buf0 = VFS_PAGE_SIZE, files1[ino0] = mkfile(m5, md1, m6, content0), files1[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf0), files0[ino0] = mkfile(m5, md1, m6, content1), (content0 ⊕ mkcontent(ino0, pcache))[n0] = content1[n0], n * VFS_PAGE_SIZE < m2, n0 ∈ content0, m ∈ files1, datakey(m, n) ∈ pcache, ino0 ∈ files0, ino0 ∈ files1, n0 ∈ content0 ⊕ mkcontent(ino0, pcache), n0 ∈ content1, ∀ n. (n ∈ content0 ⊕ mkcontent(ino0, pcache) ↔ n ∈ content1 ⊕ mkcontent(ino0, pcache0)) ∧ (n ∈ content0 ⊕ mkcontent(ino0, pcache) → (content0 ⊕ mkcontent(ino0, pcache))[n] = (content1 ⊕ mkcontent(ino0, pcache0))[n]), ∀ ino. ino ≠ m ∧ ino ∈ files0 → mkfile(files1[ino].size, files1[ino].meta, files1[ino].nlink, files1[ino].content ⊕ mkcontent(ino, pcache)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0)) ∧ ino ∈ files1 ⊦ content0[n0] = content1[n0], datakey(ino0, n0) = datakey(m, n), ino0 = m, datakey(ino0, n0) ∈ pcache, datakey(ino0, n0) ∈ pcache0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: cache-base name: at-overwrite-content-old seq: ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n] subst: [n, content1, content0] → [n0, mkcontent(ino0, pcache), content0] flags: List([[0,0,5,1,0]])

Additional information

Used simplifier rules: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]; (s)% ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page; (s)% ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s) Used terms: n0, mkcontent(ino0, pcache), content0