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Proof step 8 from proof abs-files-put (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ fs = fs0 ↔ (∀ fid. (fid ∈ fs ↔ fid ∈ fs0) ∧ fs[fid] = fs0[fid])
Proof step 10:
ino ∈ files, ∀ fid. (fid ∈ abs-files(files)[⌜ino⌝ , mkfile(md0, buf)] ↔ fid ∈ abs-files(files[ino, mkfile(m, md, m0, content)])) ∧ abs-files(files)[⌜ino⌝ , mkfile(md0, buf)][fid] = abs-files(files[ino, mkfile(m, md, m0, content)])[fid] ⊦ md0 = md ∧ buf = (content.stream to m).buf

Rule argument

spec: store, inst: file-data-store name: Extension seq: ⊦ fs = fs0 ↔ (∀ fid. (fid ∈ fs ↔ fid ∈ fs0) ∧ fs[fid] = fs0[fid]) subst: [fs0, fs] → [abs-files(files[ino, mkfile(m, md, m0, content)]), abs-files(files)[⌜ino⌝ , mkfile(md0, buf)]] flags: <all paths>

Additional information

Used terms: abs-files(files[ino, mkfile(m, md, m0, content)]), abs-files(files)[⌜ino⌝ , mkfile(md0, buf)]