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Proof step 218 from proof overwrite-write-page-dirty (previous step)

files[ino0] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ files, ino0 ∈ files, ino ∈ icache, datakey(ino0, n) ∈ pcache[datakey(ino, m), mkpentry(true, buf)] ⊦ (content0 ⊕ mkcontent(ino0, pcache))[n] = pcache[datakey(ino, m), mkpentry(true, buf)][datakey(ino0, n)].page, ino0 ∈ icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 219:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino0] = mkfile(m2, md0, m3, content0), pcache[datakey(ino, m), mkpentry(true, buf)][datakey(ino0, n)] = mkpentry(boolvar, buf0), datakey(ino0, n) ∈ pcache[datakey(ino, m), mkpentry(true, buf)], ino ∈ icache, ino0 ∈ files, ino ∈ files ⊦ (content0 ⊕ mkcontent(ino0, pcache))[n] = buf0, ino0 ∈ 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(ino0, n) ], boolvar0, 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(ino0, n)], boolvar0, buf0