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Proof step 3 from proof in-del-ro (previous step)

⊦ key ∈ (ri -- key0) \ datakeys(key0, ri) ↔ key ∈ ri ∧ key ≠ key0 ∧ (key.data? → inodekey(key.ino) ≠ key0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ key ∈ ri \ datakeys(key0, ri) ↔ key ∈ ri ∧ (key.data? → inodekey(key.ino) ≠ key0), key = key0

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ (ri -- key) \ ks = (ri \ ks) -- key; (s)