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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n ^ (m + 1) = n ^ m * n
Proof step 12:
m ^ m0 < m ^ n1 ↔ m0 < n1 ⊦ m ^ m0 * m < m ^ n1 * m ↔ m0 < n1, m = 1, m = 0

Rule argument

spec: <toplevel> name: rec-01 seq: ⊦ n ^ (m + 1) = n ^ m * n subst: [m, n] → [m0, m] flags: <all paths>

Additional information

Used terms: m0, m