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Proof step 245 from proof overwrite-write-page-dirty (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 246:
files[ino] = mkfile(m2, md0, m3, content0), ino ∈ files ⊦ (content0 ⊕ mkcontent(ino, pcache))[n] = content0[n], datakey(ino, n) = datakey(ino, m), ino ∈ icache, datakey(ino, 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)