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Proof step 249 from proof overwrite-write-page-dirty (previous step)

files[ino] = mkfile(m2, md0, m3, content0), ino ∈ files, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(true, buf)] ⊦ (content0 ⊕ mkcontent(ino, pcache))[n] = pcache[datakey(ino, m), mkpentry(true, buf)][datakey(ino, n)].page, n = m, ino ∈ icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 250:
files[ino] = mkfile(m2, md0, m3, content0), pcache[datakey(ino, m), mkpentry(true, buf)][datakey(ino, n)] = mkpentry(boolvar, buf0), datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(true, buf)], ino ∈ files ⊦ (content0 ⊕ mkcontent(ino, pcache))[n] = buf0, n = m, ino ∈ icache

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, m), mkpentry(true, buf)] [datakey(ino, n) ], boolvar, buf0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[datakey(ino, m), mkpentry(true, buf)][datakey(ino, n)], boolvar, buf0