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

files[ino0] = mkfile(m, md, m0, content), ino0 ∈ files ⊦ ino0 = ino, mkfile(md, (content.stream to m).buf) = abs-files(files -- ino)[⌜ino0⌝ ]

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] → [ino0, files -- ino] flags: <all paths>

Additional information

Used simplifier rules: ino ∈ files ⊦ ino ≠ ino0 → (files -- ino0)[ino] = files[ino]; (s)% ⊦ ino ∈ files -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ files; (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) Used terms: ino0, files -- ino