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Proof step 23 from proof at-pcache-overwrite-other (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: cache-base name: at-overwrite-content-old seq: ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n] subst: [n, content1, content0] → [n, mkcontent(ino, pcache), content] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]; (s)% ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page; (s)% ⊦ mkpentry(boolvar, buf).page = buf; (s) Used terms: n, mkcontent(ino, pcache), content