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Proof step 16 from proof abs-files-new (previous step)

ino0 ∈ files ⊦ ino = 0, mkfile(files[ino0].meta, (files[ino0].content.stream to files[ino0].size).buf) = abs-files((files ++ ino)[ino, mkfile(0, md, 1, ∅)])[⌜ino0⌝ ], ino ∈ files

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
files[ino0] = mkfile(m, md0, m0, content), ino0 ∈ files ⊦ ino = 0, mkfile(md0, (content.stream to m).buf) = abs-files((files ++ ino)[ino, mkfile(0, md, 1, ∅)])[⌜ino0⌝ ], ino ∈ files

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[ino0], m, md0, m0, 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[ino0], m, md0, m0, content