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Proof step 7 from proof lookup-append (previous step)

∀ a, ay. a ∈ ax0 → (ax0 + ay)[a] = ax0[a] ⊦ a ∈ p ', ((p ' + ax0) + ay)[a] = (p ' + ax0)[a], ¬ a ∈ p ' ∧ ¬ a ∈ ax0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information