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Proof step 1 from proof uniquelen (conclusion)

∀ a. a ∈ ax ↔ a ∈ ay, unique_al(ax), unique_al(ay) ⊦ # ax = # ay

User applied rule structural induction

And obtained the following new goals

Proof step 2:
⊦ (∀ a. a ∈ [] ↔ a ∈ ay) ∧ unique_al([]) ∧ unique_al(ay) → # [] = # ay
Proof step 8:
∀ ay. (∀ a. a ∈ ax0 ↔ a ∈ ay) ∧ unique_al(ax0) ∧ unique_al(ay) → # ax0 = # ay ⊦ (∀ a. a ∈ p + ax0 ↔ a ∈ ay) ∧ unique_al(p + ax0) ∧ unique_al(ay) → #(p + ax0) = # ay

Rule argument

indvar: ax

Additional information

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