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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.tail), ∀ a. a ∈ ax → a ∈ ay ⊦ ax = [], ax.head.1 ∈ ax.tail

Rule argument

Additional information

Used simplifier rules: k-unique-r: ⊦ unique_al(ay) ↔ ay = [] ∨ ¬ ay.head.1 ∈ ay.tail ∧ unique_al(ay.tail);% ⊦ # ax = 0 ↔ ax = []; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)