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Proof step 19 from proof at-pcache-overwrite-other (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
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] ⊦ pcache[key0, pe][datakey(ino, n)].page = (content ⊕ mkcontent(ino, pcache))[n], ino = key0.ino

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page; (s)