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Proof step 5 from proof mult (previous step)

∀ m, m0. (m * m0) ^ n0 = m ^ n0 * m0 ^ n0 ⊦ (m * m0) ^ n0 * m * m0 = m ^ (n0 + 1) * m0 ^ (n0 + 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, m0. (m * m0) ^ n0 = m ^ n0 * m0 ^ n0 ⊦ (m * m0) ^ n0 * m * m0 = m ^ (n0 + 1) * m0 ^ n0 * m0

Rule argument

spec: inst: name: rec-01 seq: ⊦ n ^ (m + 1) = n ^ m * n subst: [m, n] → [n0, m0] flags: rewrite, current

Additional information

Used terms: n0, m0