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Proof step 77 from proof fsync-pages-others-unchanged (previous step)

# buf0 = VFS_PAGE_SIZE, (content0 ⊕ mkcontent(ino0, pcache))[n0] = (content1 ⊕ mkcontent(ino0, pcache0))[n0], files0[ino0] = mkfile(m5, md1, m6, content1), pcache[datakey(m, n)] = mkpentry(true, buf0), files1[m] = mkfile(m0, md, m1, content), files1[ino0] = mkfile(m5, md1, m6, content0), n * VFS_PAGE_SIZE < m2, n0 ∈ content1 ⊕ mkcontent(ino0, pcache0), n0 ∈ content0 ⊕ mkcontent(ino0, pcache), ino0 ∈ files1, ino0 ∈ files0, datakey(m, n) ∈ pcache, m ∈ files1, n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]), ∀ 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, ∀ 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]) ⊦ (content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]))[n0] = (content1 ⊕ mkcontent(ino0, pcache0))[n0], ino0 = m, n0 ∈ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
# 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 ⊕ mkcontent(ino0, pcache0))[n0], n * VFS_PAGE_SIZE < m2, m ∈ files1, datakey(m, n) ∈ pcache, ino0 ∈ files0, ino0 ∈ files1, n0 ∈ content0 ⊕ mkcontent(ino0, pcache), n0 ∈ content1 ⊕ mkcontent(ino0, pcache0), n0 ∈ content0, ∀ 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 ⊕ mkcontent(ino0, pcache0))[n0], datakey(ino0, n0) = datakey(m, n), ino0 = m, datakey(ino0, n0) ∈ pcache

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (s)