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Proof step 226 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);mkfile(m7, md1, m8, content0)) = mkfile(m9, md2, m10, content2), n0 ∈ content0 ⊕ mkcontent(ino, pcache) ↔ n0 ∈ content1 ⊕ mkcontent(ino, pcache0), files1[ino] = mkfile(m7, md1, m8, content1), files0[ino] = mkfile(m7, md1, m8, content0), files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar0, mkinode(m3, md0, true, m4, m5, m6)), (content0 ⊕ mkcontent(ino, pcache))[n0] = (content1 ⊕ mkcontent(ino, pcache0))[n0], n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ino ∈ icache, n0 ∈ mkcontent(ino, pcache0), ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ m7 = m9 ∧ md1 = md2 ∧ m8 = m10 ∧ (n0 ∈ content1 ⊕ mkcontent(ino, pcache0) ↔ n0 ∈ content2 ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)])) ∧ ( n0 ∈ content1 ⊕ mkcontent(ino, pcache0) → (content1 ⊕ mkcontent(ino, pcache0))[n0] = (content2 ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)]))[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 227:
# buf = VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);mkfile(m7, md1, m8, content0)) = mkfile(m9, md2, m10, content2), files1[ino] = mkfile(m7, md1, m8, content1), files0[ino] = mkfile(m7, md1, m8, content0), files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar0, mkinode(m3, md0, true, m4, m5, m6)), (content0 ⊕ mkcontent(ino, pcache))[n0] = pcache0[datakey(ino, n0)].page, n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(ino, n0) ∈ pcache0, ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ino ∈ icache, n0 ∈ content0 ⊕ mkcontent(ino, pcache), n0 ∈ content1 ⊕ mkcontent(ino, pcache0), ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ m7 = m9 ∧ md1 = md2 ∧ m8 = m10 ∧ n0 ∈ content2 ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)]) ∧ (content1 ⊕ mkcontent(ino, pcache0))[n0] = (content2 ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)]))[n0]

Rule argument

Additional information

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