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Proof step 2 from proof nuni-01 (previous step)

a ∈ az, unique_al(ay + (a × d)' + az) ⊦

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a, az, d. ¬(a ∈ az ∧ unique_al(ay0 + (a × d)' + az)), a ∈ az, unique_al((p + ay0) + (a × d)' + az) ⊦

Rule argument

term: ay

Additional information

Used simplifier rules: cons: ⊦ unique_al((a × d)' + ax) ↔ ¬ a ∈ ax ∧ unique_al(ax);%assoclist freely generated by [], +;;%Nil: ⊦ [] + ax = ax; from specification list[assoclista]%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[assoclista]