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Proof step 10 from proof mult (previous step)

∀ m, m0. (m * m0) ^ n0 = m ^ n0 * m0 ^ n0 ⊦ m0 = 0, (m * m0) ^ n0 * m = (m ^ n0 * m) * m0 ^ n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
∀ m, m0. (m * m0) ^ n0 = m ^ n0 * m0 ^ n0 ⊦ m0 = 0, m = 0, (m * m0) ^ n0 = m ^ n0 * m0 ^ n0

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%zero-02: ⊦ m * n = m * n0 ↔ m = 0 ∨ n = n0; from specification nat-mult