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Proof step 208 from proof overwrite-write-page-clean (previous step)

pcache[datakey(ino, m), mkpentry(false, buf)][datakey(ino0, m)] = mkpentry(boolvar0, buf0), 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), datakey(ino0, m) ∈ pcache, ino ∈ icache, ino0 ∈ files, ino ∈ files, ino0 ∈ icache, datakey(ino0, m) ∈ pcache[datakey(ino, m), mkpentry(false, buf)] ⊦ (content1 ⊕ mkcontent(ino0, pcache))[m] = buf0, datakey(ino0, m) = datakey(ino, m), ino0 = ino, m ∈ content1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 209:
((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), pcache[datakey(ino0, m)] = mkpentry(boolvar0, buf0), ino0 ∈ icache, ino ∈ files, ino0 ∈ files, ino ∈ icache, datakey(ino0, m) ∈ pcache ⊦ (content1 ⊕ mkcontent(ino0, pcache))[m] = buf0, datakey(ino0, m) = datakey(ino, m), m ∈ content1

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)