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Proof step 1 from proof f-rm (conclusion)

⊦ filter(rmdup(x), y) = rmdup(filter(x, y))

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(a + x0), y) = rmdup(filter(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