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Proof step 11 from proof oc-filt (previous step)

a ∈ y, ∀ a, y. a ∈ y → #oc(a, filter(x0, y)) = #oc(a, x0) ⊦ #oc(a, filter(a0 ' + x0, y)) = #oc(a, x0), a0 = a, a0 ∈ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
a ∈ y, ∀ a, y. a ∈ y → #oc(a, filter(x0, y)) = #oc(a, x0) ⊦ #oc(a, filter(x0, y)) = #oc(a, x0), a0 ∈ y

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ ¬ a ∈ y → filter(a ' + x, y) = filter(x, y); (s)