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Proof step 4 from proof overwrite-write-page-clean (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino, mkfile(m0, md, m1, content[m, buf])] = (files[ino, files[ino].content:= files[ino].content[m, buf]] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino, mkfile(m0, md, m1, content[m, buf])] = (files[ino, files[ino].content:= content0[m, buf]] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[ino], m2, md0, m3, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[ino], m2, md0, m3, content0