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Proof step 3 from proof del-this (previous step)

⊦ ∀ key0. (key0 ∈ ri[key, adr] ⊖ key ↔ key0 ∈ ri ⊖ key) ∧ (key0 ∈ ri[key, adr] ⊖ key → (ri[key, adr] ⊖ key)[key0] = (ri ⊖ key)[key0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information