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Proof step 4 from proof app (previous step)

unique_al((p ' + ax0) + p0 ' + ay), ∀ p, ay. unique_al(ax0 + p ' + ay) → unique_al(ax0 + ay) ⊦ unique_al((p ' + ax0) + ay)

User applied rule structural induction

And obtained the following new goals

Proof step 5:
⊦ unique_al(((a × d)' + ax0) + p0 ' + ay) ∧ (∀ p, ay. unique_al(ax0 + p ' + ay) → unique_al(ax0 + ay)) → unique_al(((a × d)' + ax0) + ay)

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;