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Proof step 2 from proof overwrite-write-page-dirty (previous step)

ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino, ((files ⊕ pcache) ⊕ icache)[ino].content:= ((files ⊕ pcache) ⊕ icache)[ino].content[m, buf]] = (files ⊕ pcache[datakey(ino, m), mkpentry(true, buf)]) ⊕ icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino, ((files ⊕ pcache) ⊕ icache)[ino].content:= content[m, buf]] = (files ⊕ pcache[datakey(ino, m), mkpentry(true, 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 ⊕ pcache) ⊕ icache)[ino], m0, md, m1, content]

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 ⊕ pcache) ⊕ icache)[ino], m0, md, m1, content