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Proof step 11 from proof abs-files-put-nlink (previous step)

files[ino] = mkfile(m, md, n0, content), files[ino0] = mkfile(m0, md0, m1, content0), ino0 ∈ files, ino ∈ files ⊦ abs-files(files[ino, mkfile(m, md, n1, content)])[⌜ino0⌝ ] = mkfile(md0, (content0.stream to m0).buf)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile(files[ino].meta, (files[ino].content.stream to files[ino].size).buf)
Proof step 13:
files[ino0] = mkfile(m0, md0, m1, content0), files[ino] = mkfile(m, md, n0, content), ino ∈ files, ino0 ∈ files, ino0 ∈ files[ino, mkfile(m, md, n1, content)] ⊦ mkfile (files[ino, mkfile(m, md, n1, content)][ino0].meta, (files[ino, mkfile(m, md, n1, content)][ino0].content.stream to files[ino, mkfile(m, md, n1, content)][ino0].size).buf) = mkfile(md0, (content0.stream to m0).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, mkfile(m, md, n1, content)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s) Used terms: ino0, files[ino, mkfile(m, md, n1, content)]