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Proof step 214 from proof overwrite-write-page-dirty (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino0] = mkfile(m2, md0, m3, content0), ino ∈ icache, ino0 ∈ files, ino ∈ files ⊦ (content0 ⊕ mkcontent(ino0, pcache))[n] = (content0 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]))[n], ino0 ∈ icache, n ∈ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 215:
files[ino0] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ files, ino0 ∈ files, ino ∈ icache ⊦ (content0 ⊕ mkcontent(ino0, pcache))[n] = content0[n], datakey(ino0, n) = datakey(ino, m), ino0 ∈ icache, datakey(ino0, n) ∈ pcache

Rule argument

Additional information

Used simplifier rules: at-overwrite-content-old: ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n];%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws)