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Proof step 9 from proof abs-files-new (previous step)

⊦ ino = 0, mkfile(md, mkbuf(0)) = abs-files((files ++ ino)[ino, mkfile(0, md, 1, ∅)])[⌜ino⌝ ], ino ∈ files

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile(files[ino].meta, (files[ino].content.stream to files[ino].size).buf)

Rule argument

spec: <toplevel> name: abs-files-at seq: ⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile (files[ino].meta, (files[ino].content.stream to files[ino].size).buf) subst: [ino, files] → [ino, (files ++ ino)[ino, mkfile(0, md, 1, ∅)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)%ino ≠ 0, ¬ ino ∈ files ⊦ ino0 ∈ files ++ ino ↔ ino0 = ino ∨ ino0 ∈ files; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ ∅.stream = σ⊥; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ σ0 to 0 = []; (s)% ⊦ [].buf = mkbuf(0); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s) Used terms: ino, (files ++ ino)[ino, mkfile(0, md, 1, ∅)]