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Proof step 5 from proof app (previous step)

⊦ unique_al(((a × d)' + ax0) + p0 ' + ay) ∧ (∀ p, ay. unique_al(ax0 + p ' + ay) → unique_al(ax0 + ay)) → unique_al(((a × d)' + ax0) + ay)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: cons: ⊦ unique_al((a × d)' + ax) ↔ ¬ a ∈ ax ∧ unique_al(ax);% ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1;