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Proof step 386 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), datakey(ino, n) ∈ pcache, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], ino0 ∈ icache, ino ∈ icache, ino0 ∈ files, ino ∈ files, datakey(ino0, n) ∈ pcache ⊦ pcache[datakey(ino0, n)].page = (content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[n], ino0 = ino, n = m, n ∈ content0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 387:
((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(ino0, n)] = mkpentry(boolvar0, buf0), datakey(ino0, n) ∈ pcache, ino ∈ files, ino0 ∈ files, ino ∈ icache, ino0 ∈ icache, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], datakey(ino, n) ∈ pcache ⊦ buf0 = (content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[n], ino0 = ino, n = m, n ∈ content0

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[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(ino0, n)], boolvar0, buf0