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Proof step 1 from proof add (conclusion)

⊦ m ^ (n + n0) = m ^ n * m ^ n0

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ m, n. m ^ (n + n1) = m ^ n * m ^ n1 ⊦ m ^ (n + n1 +1) = m ^ n * m ^ n1 +1

Rule argument

term: n0

Additional information

Used simplifier rules: Pot-zero: ⊦ n ^ 0 = 1;%nat freely generated by 0, +1;;%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%one: ⊦ m0 * 1 = m0; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult