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Proof step 3 from proof overwrite-write-page-clean (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino, ((files ⊕ pcache) ⊕ icache)[ino].content:= content[m, buf]] = (files[ino, files[ino].content:= files[ino].content[m, buf]] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino, mkfile(m0, md, m1, content[m, buf])] = (files[ino, files[ino].content:= files[ino].content[m, buf]] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)