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Proof step 30 from proof pcache-overwrite-read-page (previous step)

pcache[datakey(ino, n), mkpentry(false, content[n])][datakey(ino0, n0)] = mkpentry(boolvar, buf), files[ino0] = mkfile(m1, md0, m2, content0), files[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files, ino0 ∈ files, datakey(ino0, n0) ∈ pcache[datakey(ino, n), mkpentry(false, content[n])] ⊦ buf = (content0 ⊕ mkcontent(ino0, pcache))[n0], datakey(ino0, n0) = datakey(ino, n), datakey(ino, n) ∈ pcache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
files[ino] = mkfile(m, md, m0, content), files[ino0] = mkfile(m1, md0, m2, content0), pcache[datakey(ino0, n0)] = mkpentry(boolvar, buf), ino0 ∈ files, ino ∈ files, n ∈ content, datakey(ino0, n0) ∈ pcache ⊦ buf = (content0 ⊕ mkcontent(ino0, pcache))[n0], datakey(ino0, n0) = datakey(ino, n), datakey(ino, n) ∈ pcache

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)