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Proof step 15 from proof eq1 (previous step)

((n0 + 1) + m) / m * m ≤ n0 + 1, ∀ m. (n0 + m) / m * m ≤ n0 → m = 0 ⊦ m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
n ≠ 0 ⊦ m % n + 1 = n → (m + 1) / n = m / n + 1

Rule argument

spec: nat-div inst: name: div-succ seq: n ≠ 0 ⊦ m % n + 1 = n → (m + 1) / n = m / n + 1 subst: [n, m] → [m, m + n0] flags: rewrite

Additional information

[Concretesimprules((Csimpnamedseq(nat-basic2,,a, ⊦ (m + n0) + n1 = m + n0 + n1) Csimpnamedseq(nat-basic2,,c, ⊦ m + n = n + m))), Extraterms((mm + n0))]