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Proof step 21 from proof pcache-overwrite-read-page (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
files[ino0] = mkfile(m1, md0, m2, content0), files[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files, ino0 ∈ files ⊦ content0[n0] = (content0 ⊕ mkcontent(ino0, pcache))[n0], datakey(ino0, n0) = datakey(ino, n), datakey(ino, n) ∈ pcache, datakey(ino0, n0) ∈ 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)