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Proof step 2 from proof uniquelen (previous step)

⊦ (∀ a. a ∈ [] ↔ a ∈ ay) ∧ unique_al([]) ∧ unique_al(ay) → # [] = # ay

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
unique_al(ay), ∀ a. ¬ a ∈ ay ⊦ ay = []

Rule argument

Additional information

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