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Proof step 13 from proof abs-files-put (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ 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, mkfile(m, md, m0, content)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(md, buf) = mkfile(md0, buf0) ↔ md = md0 ∧ buf = buf0; (ws)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s) Used terms: ino, files[ino, mkfile(m, md, m0, content)]