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Proof step 73 from proof fsync-pages-others-unchanged (previous step)

# buf0 = VFS_PAGE_SIZE, n0 ∈ content0 ⊕ mkcontent(ino0, pcache) ↔ n0 ∈ content1 ⊕ mkcontent(ino0, pcache0), 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, ino0 ∈ files1, ino0 ∈ files0, datakey(m, n) ∈ pcache, m ∈ files1, n0 ∈ content1 ⊕ mkcontent(ino0, pcache0) → (content0 ⊕ mkcontent(ino0, pcache))[n0] = (content1 ⊕ mkcontent(ino0, pcache0))[n0], ∀ 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]) ⊦ ino0 = m, (n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]) ↔ n0 ∈ content1 ⊕ mkcontent(ino0, pcache0)) ∧ ( n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]) → (content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]))[n0] = (content1 ⊕ mkcontent(ino0, pcache0))[n0])

User applied rule case distinction

And obtained the following new goals

Proof step 74:
# buf0 = VFS_PAGE_SIZE, n0 ∈ content0 ⊕ mkcontent(ino0, pcache) ↔ n0 ∈ content1 ⊕ mkcontent(ino0, pcache0), 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), n * VFS_PAGE_SIZE < m2, n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]), m ∈ files1, datakey(m, n) ∈ pcache, ino0 ∈ files0, ino0 ∈ files1, n0 ∈ content1 ⊕ mkcontent(ino0, pcache0) → (content0 ⊕ mkcontent(ino0, pcache))[n0] = (content1 ⊕ mkcontent(ino0, pcache0))[n0], ∀ 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 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]))[n0] = (content1 ⊕ mkcontent(ino0, pcache0))[n0], ino0 = m

Rule argument

pos: right 2

Additional information

Used simplifier rules: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws)% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)