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Proof step 1 from proof le (conclusion)

⊦ # filter(rmdup(x), y) ≤ # y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# y < # filter(rmdup(x), y) ⊦ filter(rmdup(x), 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