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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
⊦ ⌜ino⌝ ∈ abs-files(files) ↔ ino ∈ files
Proof step 13:
mkfile(md0, buf) = abs-files(files[ino, mkfile(m, md, m0, content)])[⌜ino⌝ ], ino ∈ files ⊦ md0 = md ∧ buf = (content.stream to m).buf

Rule argument

Additional information

Used simplifier rules: abs-files-in: ⊦ ⌜ino⌝ ∈ abs-files(files) ↔ ino ∈ files;% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ fid ∈ fs[fid, f]; (s)% ⊦ fs[fid, f][fid] = f; (s)