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Proof step 9 from proof unique-put (previous step)

∀ a, d. unique_al(ax0[a, d]) ↔ unique_al(ax0) ⊦ a = a0, ¬ a0 ∈ ax0 ∧ unique_al(ax0[a, d]) ↔ ¬ a0 ∈ ax0 ∧ unique_al(ax0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information