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Proof step 323 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, n0 ∈ content2 ↔ n0 ∈ content1, files1[ino] = mkfile(m7, md1, m8, content1), files0[ino] = mkfile(m7, md1, m8, content2), 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)), content2[n0] = content1[n0], n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ino ∈ icache, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ datakey(ino, n0) = datakey(m, n), ino = m, datakey(ino, n0) ∈ pcache, datakey(ino, n0) ∈ pcache0, (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 nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 324:
# buf = VFS_PAGE_SIZE, n0 ∈ content2 ↔ n0 ∈ content1, content2[n0] = content1[n0], icache[ino] = mkientry(boolvar0, mkinode(m3, md0, true, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, m1, content), files0[ino] = mkfile(m7, md1, m8, content2), files1[ino] = mkfile(m7, md1, m8, content1), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ icache, m ∈ files0, datakey(m, n) ∈ pcache, ino ∈ files1, ino ∈ files0, n0 ∈ content2, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ datakey(ino, n0) = datakey(m, n), ino = m, datakey(ino, n0) ∈ pcache0, datakey(ino, n0) ∈ pcache, (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])

Rule argument

fma: n0 ∈ content2

Additional information

Used simplifier rules: ⊦ ¬ n ∈ content → content[n] = (∅)[n]; (s)% ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ key ≠ key0 → (key ∈ pcache[key0, pe] ↔ key ∈ pcache); (s) Used formulas: n0 ∈ content2