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Proof step 1 from proof ocappend (conclusion)

⊦ #oc(a, x + y) = #oc(a, x) + #oc(a, y)

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ a, y. #oc(a, x0 + y) = #oc(a, x0) + #oc(a, y) ⊦ #oc(a, (a0 + x0) + y) = #oc(a, a0 + x0) + #oc(a, y)

Rule argument

indvar: x

Additional information

Used simplifier rules: oc-e: ⊦ #oc(a, []) = 0;%list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2