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Proof step 20 from proof abs-files-new (previous step)

files[ino0] = mkfile(m, md0, m0, content), ino0 ∈ files ⊦ ino = 0, mkfile(md0, (content.stream to m).buf) = mkfile((files ++ ino)[ino0].meta, ((files ++ ino)[ino0].content.stream to (files ++ ino)[ino0].size).buf), ino ∈ files

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
files[ino0] = mkfile(m, md0, m0, content), (files ++ ino)[ino0] = mkfile(m1, md, m2, content0), ino0 ∈ files ⊦ ino = 0, mkfile(md0, (content.stream to m).buf) = mkfile(md, (content0.stream to m1).buf), 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 ++ ino)[ino0], m1, md, m2, 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)[ino0], m1, md, m2, content0