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Proof step 1 from proof dups-lesize (conclusion)

¬ dups(x), ¬ dups(y), ∀ a. a ∈ x → a ∈ y ⊦ # x ≤ # y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# y < # x, ∀ a. a ∈ x → a ∈ y ⊦ x = [], dups(x), dups(y)

Rule argument

Additional information

Used simplifier rules: l: ⊦ # x = 0 ↔ x = []; from specification list-data%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat