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Proof step 9 from proof add (previous step)

∀ m, n. m ^ (n + n1) = m ^ n * m ^ n1 ⊦ m ^ (n1 + n) * m = m ^ n * m ^ n1 * m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
∀ m, n. m ^ (n + n1) = m ^ n * m ^ n1 ⊦ m = 0, m ^ (n1 + n) = m ^ n * m ^ n1

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