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Proof step 1 from proof lenle (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# ay < # ax, unique_al(ax.rest), ∀ a. a ∈ ax → a ∈ ay ⊦ ax = [], ax.first.1 ∈ ax.rest

Rule argument

Additional information

Used simplifier rules: k-unique-r: ⊦ unique_al(ay) ↔ ay = [] ∨ ¬ ay.first.1 ∈ ay.rest ∧ unique_al(ay.rest);%l: ⊦ # ax = 0 ↔ ax = []; from specification list-data[assoclista]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat