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Proof step 409 from proof overwrite-write-page-clean (previous step)

files[ino0] = mkfile(m8, md2, m9, content1), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, false, m5, m6, m7)), files[ino] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), pcache[datakey(ino0, n)] = mkpentry(boolvar0, buf0), datakey(ino0, n) ∈ pcache, ino0 ∈ icache, ino ∈ icache, ino0 ∈ files, ino ∈ files, n ∈ content0[m, buf], datakey(ino0, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)] ⊦ buf0 = pcache[datakey(ino, m), mkpentry(false, buf)][datakey(ino0, n)].page, datakey(ino, n) = datakey(ino, m), datakey(ino, n) ∈ pcache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 410:
pcache[datakey(ino0, n)] = mkpentry(boolvar0, buf0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, false, m5, m6, m7)), files[ino0] = mkfile(m8, md2, m9, content1), pcache[datakey(ino, m), mkpentry(false, buf)][datakey(ino0, n)] = mkpentry(boolvar1, buf1), datakey(ino0, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], n ∈ content0[m, buf], ino ∈ files, ino0 ∈ files, ino ∈ icache, ino0 ∈ icache, datakey(ino0, n) ∈ pcache ⊦ buf0 = buf1, datakey(ino, n) = datakey(ino, m), 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, m), mkpentry(false, buf)] [datakey(ino0, n) ], boolvar1, buf1]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[datakey(ino, m), mkpentry(false, buf)][datakey(ino0, n)], boolvar1, buf1