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Proof step 17 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) = abs-files((files ++ ino)[ino, mkfile(0, md, 1, ∅)])[⌜ino0⌝ ], ino ∈ files

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile(files[ino].meta, (files[ino].content.stream to files[ino].size).buf)
Proof step 19:
files[ino0] = mkfile(m, md0, m0, content), ino0 ∈ files, ino0 ∈ (files ++ ino)[ino, mkfile(0, md, 1, ∅)] ⊦ ino = 0, mkfile(md0, (content.stream to m).buf) = mkfile ((files ++ ino)[ino, mkfile(0, md, 1, ∅)][ino0].meta, ((files ++ ino)[ino, mkfile(0, md, 1, ∅)][ino0].content.stream to (files ++ ino)[ino, mkfile(0, md, 1, ∅)][ino0].size).buf), ino ∈ files

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] → [ino0, (files ++ ino)[ino, mkfile(0, md, 1, ∅)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)%ino ≠ 0, ¬ ino ∈ files ⊦ ino0 ∈ files ++ ino ↔ ino0 = ino ∨ ino0 ∈ files; (s) Used terms: ino0, (files ++ ino)[ino, mkfile(0, md, 1, ∅)]