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Proof step 2 from proof app (previous step)

unique_al(ax + p ' + ay) ⊦ unique_al(ax + ay)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ p, ay. unique_al(ax0 + p ' + ay) → unique_al(ax0 + ay) ⊦ unique_al((p + ax0) + p0 ' + ay) → unique_al((p + ax0) + ay)

Rule argument

term: ax

Additional information

Used simplifier rules: not: ⊦ ¬ unique_al(ax) → ¬ unique_al(p ' + ax);%assoclist freely generated by [], +;;% ⊦ [] + ax = ax;% ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1;