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Proof step 22 from proof at-pcache-overwrite-other (previous step)

pcache[key0, pe][datakey(ino, n)] = mkpentry(boolvar, buf), files[ino] = mkfile(m, md, m0, content), n ∈ content ⊕ mkcontent(ino, pcache), n ∈ content ⊕ mkcontent(ino, pcache[key0, pe]), datakey(ino, n) ∈ pcache[key0, pe] ⊦ buf = (content ⊕ mkcontent(ino, pcache))[n], datakey(ino, n) = key0, ino = key0.ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
files[ino] = mkfile(m, md, m0, content), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), n ∈ content ⊕ mkcontent(ino, pcache[key0, pe]), n ∈ content ⊕ mkcontent(ino, pcache), datakey(ino, n) ∈ pcache ⊦ buf = (content ⊕ mkcontent(ino, pcache))[n], datakey(ino, n) = key0, ino = key0.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)