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Proof step 4 from proof unique (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ a, d. unique_al(ax0 + (a × d)') → ax0 = [] ∨ ¬ ax0.first.1 ∈ ax0.rest ∧ unique_al(ax0.rest), unique_al((p + ax0) + (a × d)') ⊦ p + ax0 = [], ¬ (p + ax0).first.1 ∈ (p + ax0).rest ∧ unique_al((p + ax0).rest)

Rule argument

indvar: ax

Additional information

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