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Proof step 1 from proof lenequal (conclusion)

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

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ ay, b. unique_al(ax0) ∧ unique_al(ay) ∧ # ax0 = # ay ∧ (∀ a. a ∈ ax0 → a ∈ ay) ∧ b ∈ ay → b ∈ ax0 ⊦ unique_al(p + ax0) ∧ unique_al(ay) ∧ #(p + ax0) = # ay ∧ (∀ a. a ∈ p + ax0 → a ∈ ay) ∧ b ∈ ay → b ∈ p + ax0

Rule argument

indvar: ax

Additional information

Used simplifier rules: unique-e: ⊦ unique_al([]);%empty: ⊦ ¬ a ∈ [];%assoclist freely generated by [], +;;% ⊦ # [] = 0;% ⊦ # ax = 0 ↔ ax = [];