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Proof step 25 from proof pcache-overwrite-read-page (previous step)

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])] ⊦ pcache[datakey(ino, n), mkpentry(false, content[n])][datakey(ino0, n0)].page = (content0 ⊕ mkcontent(ino0, pcache))[n0], datakey(ino, n) ∈ pcache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
files[ino] = mkfile(m, md, m0, content), files[ino0] = mkfile(m1, md0, m2, content0), pcache[datakey(ino, n), mkpentry(false, content[n])][datakey(ino0, n0)] = mkpentry(boolvar, buf), datakey(ino0, n0) ∈ pcache[datakey(ino, n), mkpentry(false, content[n])], ino0 ∈ files, ino ∈ files, n ∈ content ⊦ buf = (content0 ⊕ mkcontent(ino0, pcache))[n0], datakey(ino, n) ∈ pcache

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[datakey(ino, n), mkpentry(false, content[n])] [datakey(ino0, n0) ], boolvar, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[datakey(ino, n), mkpentry(false, content[n])] [datakey(ino0, n0) ], boolvar, buf