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Proof step 2 from proof le (previous step)

# y < # filter(rmdup(x), y) ⊦ filter(rmdup(x), y) = []

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ y. # y < # filter(rmdup(x0), y) → filter(rmdup(x0), y) = [], # y < # filter(rmdup(a + x0), y) ⊦ filter(rmdup(a + x0), y) = []

Rule argument

indvar: x

Additional information

Used simplifier rules: filt-e: ⊦ filter([], y) = [];%list freely generated by [], +;;%rmdup-e: ⊦ rmdup([]) = []; from specification list-dup