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Proof step 5 from proof add (previous step)

∀ m, n. m ^ (n + n1) = m ^ n * m ^ n1 ⊦ m ^ ((n1 + 1) + n) = m ^ n * m ^ (n1 + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ n ^ (m + 1) = n ^ m * n
Proof step 7:
∀ m, n. m ^ (n + n1) = m ^ n * m ^ n1 ⊦ m ^ (n1 + n) * m = m ^ n * m ^ (n1 + 1)

Rule argument

spec: inst: name: rec-01 seq: ⊦ n ^ (m + 1) = n ^ m * n subst: [m, n] → [n1 + n, m] flags: rewrite, current

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: n1 + n, m