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Proof step 24 from proof abs-files-put (previous step)

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⌝ ])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
ino ∈ files, ⌜ino0⌝ ∈ abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)] ⊦ ino0 ∈ files

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)