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Proof step 212 from proof overwrite-write-page-clean (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, true, m5, m6, m7)), files[ino0] = mkfile(m8, md2, m9, content1), ino0 ∈ icache, ino ∈ files, ino0 ∈ files, ino ∈ icache ⊦ ino0 = ino, m ∈ content1, datakey(ino0, m) ∈ pcache, (datakey(ino0, m) = datakey(ino, m) → m ∈ content1 ⊕ mkcontent(ino0, pcache)) ∧ (content1 ⊕ mkcontent(ino0, pcache))[m] = (content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[m]

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 213:
files[ino0] = mkfile(m8, md2, m9, content1), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, true, m5, m6, m7)), files[ino] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ icache, ino0 ∈ files, ino ∈ files, ino0 ∈ icache ⊦ datakey(ino0, m) = datakey(ino, m), ino0 = ino, datakey(ino0, m) ∈ pcache, m ∈ content1, (datakey(ino0, m) = datakey(ino, m) → m ∈ content1 ⊕ mkcontent(ino0, pcache)) ∧ (content1 ⊕ mkcontent(ino0, pcache))[m] = (content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[m]

Rule argument

fma: datakey(ino0, m) = datakey(ino, m)

Additional information

Used simplifier rules: ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws) Used formulas: datakey(ino0, m) = datakey(ino, m)