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Proof step 375 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(m11, md3, m12, content2), files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar, mkinode(m3, md0, false, m4, m5, m6)), files0[ino] = mkfile(m7, md1, m8, content0), files1[ino] = mkfile(m9, md2, m10, content1), pcache0[datakey(ino, n0)] = mkpentry(boolvar0, content0[n0]), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), n0 ∈ content1 ⊕ mkcontent(ino, pcache0), datakey(ino, n0) ∈ pcache0, ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ino ∈ icache, n0 ∈ content0, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ datakey(ino, n0) ∈ pcache, 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]

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 376:
# buf = VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);mkfile(m7, md1, m8, content0)) = mkfile(m11, md3, m12, content2), pcache0[datakey(ino, n0)] = mkpentry(boolvar0, content0[n0]), files1[ino] = mkfile(m9, md2, m10, content1), files0[ino] = mkfile(m7, md1, m8, content0), icache[ino] = mkientry(boolvar, mkinode(m3, md0, false, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, m1, content), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), n0 ∈ content0, ino ∈ icache, m ∈ files0, datakey(m, n) ∈ pcache, ino ∈ files1, ino ∈ files0, datakey(ino, n0) ∈ pcache0, n0 ∈ content1 ⊕ mkcontent(ino, pcache0), ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ datakey(ino, n0) ∈ pcache, n0 ∈ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)]), 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

fma: n0 ∈ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)])

Additional information

Used simplifier rules: ⊦ 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) Used formulas: n0 ∈ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)])