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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.rest), ∀ a. ¬ a ∈ ay ⊦ ay = [], ay.first.1 ∈ ay.rest

Rule argument

Additional information

Used simplifier rules: unique-e: ⊦ unique_al([]);%k-unique-r: ⊦ unique_al(ay) ↔ ay = [] ∨ ¬ ay.first.1 ∈ ay.rest ∧ unique_al(ay.rest);%empty: ⊦ ¬ a ∈ [];%l: ⊦ # ax = 0 ↔ ax = []; from specification list-data[assoclista]%size-01: ⊦ # [] = 0; from specification list-data[assoclista]