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Proof step 3 from proof le (previous step)

∀ y. # y < # filter(rmdup(x0), y) → filter(rmdup(x0), y) = [], # y < # filter(rmdup(a + x0), y) ⊦ filter(rmdup(a + x0), y) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
# y < # filter(rmdup(a ' + x0), y), ∀ y. # y < # filter(rmdup(x0), y) → filter(rmdup(x0), y) = [] ⊦ filter(rmdup(a ' + x0), 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%c: ⊦ a + x = a ' + x; from specification list