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Proof step 6 from proof abs-files-put-nlink (previous step)

files[ino] = mkfile(m, md, n0, content), ino ∈ files ⊦ (fid ∈ abs-files(files[ino, mkfile(m, md, n1, content)]) ↔ fid ∈ abs-files(files)) ∧ (fid ∈ abs-files(files[ino, mkfile(m, md, n1, content)]) → abs-files(files[ino, mkfile(m, md, n1, content)])[fid] = abs-files(files)[fid])

User applied rule constructor cut

And obtained the following new goals

Proof step 7:
files[ino] = mkfile(m, md, n0, content), fid = ⌜ino0⌝ , ino ∈ files ⊦ (fid ∈ abs-files(files[ino, mkfile(m, md, n1, content)]) ↔ fid ∈ abs-files(files)) ∧ (fid ∈ abs-files(files[ino, mkfile(m, md, n1, content)]) → abs-files(files[ino, mkfile(m, md, n1, content)])[fid] = abs-files(files)[fid])

Rule argument

var: fid

Additional information

Used simplifier rules: fid freely generated by ⌜ ⌝;;