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Proof step 12 from proof oc-filt (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
a0 ∈ y, a ∈ y, ∀ a, y. a ∈ y → #oc(a, filter(x0, y)) = #oc(a, x0) ⊦ a0 = a, #oc(a, filter(x0, y)) = #oc(a, x0)

Rule argument

Additional information

Used simplifier rules: oc-n: ⊦ a ≠ b → #oc(a, b ' + x) = #oc(a, x);%a: ⊦ (x + y) + z = x + y + z; from specification list