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Proof step 5 from proof unique (previous step)

unique_al(ax + (a × d)') ⊦ ax = [], ¬ ax.head.1 ∈ ax.tail ∧ unique_al(ax.tail)

User applied rule structural induction

And obtained the following new goals

Proof step 6:
unique_al((p + ax0) + (a × d)'), ∀ a, d. unique_al(ax0 + (a × d)') → ax0 = [] ∨ ¬ ax0.head.1 ∈ ax0.tail ∧ unique_al(ax0.tail) ⊦ p + ax0 = [], ¬ (p + ax0).head.1 ∈ (p + ax0).tail ∧ unique_al((p + ax0).tail)

Rule argument

indvar: ax

Additional information

Used simplifier rules: assoclist freely generated by [], +;;