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Proof step 20 from proof at-pcache-overwrite-other (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
files[ino] = mkfile(m, md, m0, content), pcache[key0, pe][datakey(ino, n)] = mkpentry(boolvar, buf), datakey(ino, n) ∈ pcache[key0, pe], n ∈ content ⊕ mkcontent(ino, pcache[key0, pe]), n ∈ content ⊕ mkcontent(ino, pcache) ⊦ buf = (content ⊕ mkcontent(ino, pcache))[n], ino = key0.ino

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[key0, pe][datakey(ino, n)], boolvar, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[key0, pe][datakey(ino, n)], boolvar, buf