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Proof step 3 from proof prod-eq-zero (previous step)

Π nats0 = 0 ↔ 0 ∈ nats0 ⊦ m * Π nats0 = 0 ↔ 0 = m ∨ 0 ∈ nats0

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;