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Proof step 10 from proof abs-files-put (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 11:
⌜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

Rule argument

pos: left 2 terms: ⌜ino⌝ abort: F discard: T computed: T

Additional information

Used terms: ⌜ino⌝