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Proof step 5 from proof abs-files-put (previous step)

ino ∈ files ⊦ abs-files(files)[⌜ino⌝ , f] = abs-files(files[ino, mkfile(m, md, m0, content)]) ↔ f.meta = md ∧ f.content = (content.stream to m).buf

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
f = mkfile(md0, buf), ino ∈ files ⊦ abs-files(files)[⌜ino⌝ , f] = abs-files(files[ino, mkfile(m, md, m0, content)]) ↔ md0 = md ∧ buf = (content.stream to m).buf

Rule argument

spec: file-data name: elim seq: ⊦ md = f.meta ∧ buf = f.content ↔ f = mkfile(md, buf) subst: [f, md, buf] → [f, md0, buf]

Additional information

Used simplifier rules: ⊦ md = f.meta ∧ buf = f.content ↔ f = mkfile(md, buf); (elim) Used terms: f, md0, buf