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Proof step 1 from proof prod-app (conclusion)

⊦ Π(nats + nats0) = Π nats * Π nats0

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ nats1. Π(nats0 + nats1) = Π nats0 * Π nats1 ⊦ Π((m + nats0) + nats1) = Π(m + nats0) * Π nats1

Rule argument

indvar: nats

Additional information

Used simplifier rules: prod-empty: ⊦ Π [] = 1;%natlist freely generated by [], +;;% ⊦ [] + nats = nats;% ⊦ (nats + nats0) + nats1 = nats + nats0 + nats1;% ⊦ m0 * 1 = m0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;