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Proof step 6 from proof unique (previous step)

unique_al((p ' + ax0) + (a × d)'), (∃ a, d. unique_al(ax0 + (a × d)')) → ax0 = [] ∨ ¬ ax0.first.1 ∈ ax0.rest ∧ unique_al(ax0.rest) ⊦ ¬ p.1 ∈ ax0 ∧ unique_al(ax0)

User applied rule structural induction

And obtained the following new goals

Proof step 7:
unique_al(((a0 × d0)' + ax0) + (a × d)'), (∃ a, d. unique_al(ax0 + (a × d)')) → ax0 = [] ∨ ¬ ax0.first.1 ∈ ax0.rest ∧ unique_al(ax0.rest) ⊦ ¬ (a0 × d0).1 ∈ ax0 ∧ unique_al(ax0)

Rule argument

indvar: p

Additional information

Used simplifier rules: pair freely generated by ×;;