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Proof step 8 from proof abs-files-cong (previous step)

∀ ino. (ino ∈ files0 ↔ ino ∈ files1) ∧ ( ino ∈ files0 → files0[ino].size = files1[ino].size ∧ files0[ino].meta = files1[ino].meta ∧ files0[ino].nlink = files1[ino].nlink ∧ files0[ino].content.stream to files0[ino].size = files1[ino].content.stream to files1[ino].size) ⊦ (fid ∈ abs-files(files0) ↔ fid ∈ abs-files(files1)) ∧ (fid ∈ abs-files(files0) → abs-files(files0)[fid] = abs-files(files1)[fid])

User applied rule constructor cut

And obtained the following new goals

Proof step 9:
fid = ⌜m⌝ , ∀ ino. (ino ∈ files0 ↔ ino ∈ files1) ∧ ( ino ∈ files0 → files0[ino].size = files1[ino].size ∧ files0[ino].meta = files1[ino].meta ∧ files0[ino].nlink = files1[ino].nlink ∧ files0[ino].content.stream to files0[ino].size = files1[ino].content.stream to files1[ino].size) ⊦ (fid ∈ abs-files(files0) ↔ fid ∈ abs-files(files1)) ∧ (fid ∈ abs-files(files0) → abs-files(files0)[fid] = abs-files(files1)[fid])

Rule argument

var: fid

Additional information

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