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Proof step 7 from proof abs-files-put (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 8:
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
Proof step 15:
buf = (content.stream to m).buf, md0 = md, ino ∈ files ⊦ abs-files(files)[⌜ino⌝ , mkfile(md0, buf)] = abs-files(files[ino, mkfile(m, md, m0, content)])

Rule argument

pos: right 1

Proof step 7 from proof abs-files-put (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information