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Proof step 10 from proof le (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
# y < # filter(rmdup(x0), y), ∀ y. # y < # filter(rmdup(x0), y) → filter(rmdup(x0), y) = [] ⊦ filter(rmdup(x0), y) = [], a ∈ x0, a ∈ y

Rule argument

Additional information

Used simplifier rules: filt-n: ⊦ ¬ a ∈ y → filter(a ' + x, y) = filter(x, y);%l: ⊦ # x = 0 ↔ x = []; from specification list-data%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%a: ⊦ (x + y) + z = x + y + z; from specification list