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

key ∈ ks ⊦ # ks = 0, ks = ∅, ∀ key0. (key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ ri ⊖ ks) ∧ (key0 ∈ (ri ⊖ key) ⊖ ks → ((ri ⊖ key) ⊖ ks)[key0] = (ri ⊖ ks)[key0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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