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Proof step 22 from proof abs-files-put (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile(files[ino].meta, (files[ino].content.stream to files[ino].size).buf)
Proof step 24:
ino ∈ files ⊦ ino0 ∈ files[ino, mkfile(m, md, m0, content)], (⌜ino0⌝ ∈ abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)] ↔ ino0 ∈ files) ∧ ( ⌜ino0⌝ ∈ abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)] → abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)][⌜ino0⌝ ] = abs-files(files[ino, mkfile(m, md, m0, content)])[⌜ino0⌝ ])
Proof step 28:
ino ∈ files, ino0 ∈ files[ino, mkfile(m, md, m0, content)] ⊦ (⌜ino0⌝ ∈ abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)] ↔ ino0 ∈ files) ∧ ( ⌜ino0⌝ ∈ abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)] → abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)][⌜ino0⌝ ] = mkfile (files[ino, mkfile(m, md, m0, content)][ino0].meta, (files[ino, mkfile(m, md, m0, content)][ino0].content.stream to files[ino, mkfile(m, md, m0, content)][ino0].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, mkfile(m, md, m0, content)]] flags: <all paths>

Additional information

Used terms: ino0, files[ino, mkfile(m, md, m0, content)]