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Proof step 177 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, n0 ∈ content ↔ n0 ∈ content1, files0[m] = mkfile(m9, md2, m10, content), files1[m] = mkfile(m9, md2, m10, content1), content[n0] = content1[n0], (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ datakey(m, n0) = datakey(m, n), m ∈ icache, datakey(m, n0) ∈ pcache0, datakey(m, n0) ∈ pcache, (n0 ∈ content1 ⊕ mkcontent(m, pcache0) ↔ n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)])) ∧ ( n0 ∈ content1 ⊕ mkcontent(m, pcache0) → (content1 ⊕ mkcontent(m, pcache0))[n0] = (content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]))[n0])

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 178:
# buf = VFS_PAGE_SIZE, n0 ∈ content ↔ n0 ∈ content1, pcache[datakey(m, n)] = mkpentry(true, buf), (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), content[n0] = content1[n0], files1[m] = mkfile(m9, md2, m10, content1), files0[m] = mkfile(m9, md2, m10, content), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ datakey(m, n0) = datakey(m, n), datakey(m, n0) ∈ pcache, datakey(m, n0) ∈ pcache0, m ∈ icache, n0 ∈ mkcontent(m, pcache0), (n0 ∈ content1 ⊕ mkcontent(m, pcache0) ↔ n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)])) ∧ ( n0 ∈ content1 ⊕ mkcontent(m, pcache0) → (content1 ⊕ mkcontent(m, pcache0))[n0] = (content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]))[n0])

Rule argument

fma: n0 ∈ mkcontent(m, pcache0)

Additional information

Used simplifier rules: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s) Used formulas: n0 ∈ mkcontent(m, pcache0)