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Proof step 3 from proof oc-filt (previous step)

a ∈ y ⊦ #oc(a, filter(x, y)) = #oc(a, x)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
a ∈ y, ∀ a, y. a ∈ y → #oc(a, filter(x0, y)) = #oc(a, x0) ⊦ #oc(a, filter(a0 + x0, y)) = #oc(a, a0 + x0)

Rule argument

indvar: x

Additional information

Used simplifier rules: oc-e: ⊦ #oc(a, []) = 0;%list freely generated by [], +;;% ⊦ filter([], y) = []; (s)