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Proof step 10 from proof pot-mon (previous step)

m ^ m0 < m ^ n1 ↔ m0 < n1 ⊦ m = 1, m = 0, m ^ (m0 + 1) < m ^ n1 * m ↔ m0 < n1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n ^ (m + 1) = n ^ m * n

Rule argument

spec: inst: name: rec-01 seq: ⊦ n ^ (m + 1) = n ^ m * n subst: [m, n] → [m0, m] flags: rewrite, current

Additional information

Used simplifier rules: ls-02: ⊦ m0 ≠ 0 → (m0 * m < m0 * n ↔ m < n); 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 Used terms: m0, m