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Proof step 123 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, 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), (∅)[ino] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), pcache0[datakey(ino, n0)] = mkpentry(boolvar1, buf0), pcache[datakey(ino, n0)] = mkpentry(boolvar2, buf0), pcache[datakey(m, n), mkpentry(false, buf)][datakey(ino, n0)] = mkpentry(boolvar3, buf1), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(ino, n0) ∈ pcache[datakey(m, n), mkpentry(false, buf)], n0 ∈ content2 ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)]), datakey(ino, n0) ∈ pcache0, ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, n0 ∈ content2 ⊕ mkcontent(ino, pcache), n0 ∈ content1 ⊕ mkcontent(ino, pcache0), datakey(ino, n0) ∈ pcache, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(ino, pcache0))[n0] = buf1, ino = m, ino ∈ icache

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 124:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, n), mkpentry(false, buf)][datakey(ino, n0)] = mkpentry(boolvar3, buf1), pcache[datakey(ino, n0)] = mkpentry(boolvar2, buf0), pcache0[datakey(ino, n0)] = mkpentry(boolvar1, buf0), (∅)[ino] = mkientry(boolvar0, mkinode(m3, md0, boolvar, 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), datakey(ino, n0) ∈ pcache, n0 ∈ content1 ⊕ mkcontent(ino, pcache0), n0 ∈ content2 ⊕ mkcontent(ino, pcache), m ∈ files0, datakey(m, n) ∈ pcache, ino ∈ files1, ino ∈ files0, datakey(ino, n0) ∈ pcache0, n0 ∈ content2 ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)]), datakey(ino, n0) ∈ pcache[datakey(m, n), mkpentry(false, buf)], ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(ino, pcache0))[n0] = buf1, datakey(ino, n0) = datakey(m, n), ino = m, ino ∈ icache

Rule argument

fma: datakey(ino, n0) = datakey(m, n)

Additional information

Used simplifier rules: ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws) Used formulas: datakey(ino, n0) = datakey(m, n)