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Proof step 132 from proof overwrite-write-page-dirty (previous step)

pcache[datakey(ino, m), mkpentry(true, buf)][datakey(ino0, n)] = mkpentry(boolvar0, buf0), files[ino0] = mkfile(m6, md1, m7, content0), icache[ino0] = mkientry(boolvar, mkinode(m2, md0, false, m3, m4, m5)), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino0 ∈ icache, ino ∈ icache, ino0 ∈ files, ino ∈ files, datakey(ino0, n) ∈ pcache[datakey(ino, m), mkpentry(true, buf)] ⊦ (content0 ⊕ mkcontent(ino0, pcache))[n] = buf0, datakey(ino0, n) = datakey(ino, m), ino0 = ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 133:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), icache[ino0] = mkientry(boolvar, mkinode(m2, md0, false, m3, m4, m5)), files[ino0] = mkfile(m6, md1, m7, content0), pcache[datakey(ino0, n)] = mkpentry(boolvar0, buf0), ino ∈ files, ino0 ∈ files, ino ∈ icache, ino0 ∈ icache, datakey(ino0, n) ∈ pcache ⊦ (content0 ⊕ mkcontent(ino0, pcache))[n] = buf0, datakey(ino0, n) = datakey(ino, m), ino0 = ino

Rule argument

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (key ∈ pcache[key0, pe] ↔ key ∈ pcache); (s)% ⊦ key ≠ key0 → pcache[key0, pe][key] = pcache[key]; (s)