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Proof step 2 from proof unique-01 (previous step)

a ∈ ax, unique_al(ax + (a × d)'), unique_al(ax) ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a, d. ¬(a ∈ ax0 ∧ unique_al(ax0 + (a × d)') ∧ unique_al(ax0)), a ∈ p + ax0, unique_al((p + ax0) + (a × d)'), unique_al(p + ax0) ⊦

Rule argument

indvar: ax

Additional information

Used simplifier rules: empty: ⊦ ¬ a ∈ [];%assoclist freely generated by [], +;;