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Proof step 2 from proof prod-app (previous step)

∀ nats1. Π(nats0 + nats1) = Π nats0 * Π nats1 ⊦ Π((m + nats0) + nats1) = Π(m + nats0) * Π nats1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ nats1. Π(nats0 + nats1) = Π nats0 * Π nats1 ⊦ m = 0, Π(nats0 + nats1) = Π nats1 * Π nats0

Rule argument

Additional information

Used simplifier rules: prod-rec: ⊦ Π(n ' + nats) = n * Π nats;% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = m * n0 ↔ m = 0 ∨ n = n0;% ⊦ (nats + nats0) + nats1 = nats + nats0 + nats1;% ⊦ m + nats = m ' + nats;