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Proof step 18 from proof abs-files-put (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
ino ∈ files ⊦ (fid ∈ abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)] ↔ fid ∈ abs-files(files[ino, mkfile(m, md, m0, content)])) ∧ ( fid ∈ abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)] → abs-files(files)[⌜ino⌝ , mkfile(md, (content.stream to m).buf)][fid] = abs-files(files[ino, mkfile(m, md, m0, content)])[fid])

Proof step 18 from proof abs-files-put (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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