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Proof step 5 from proof del-commute-dels (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information