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Proof step 2 from proof div-mult-to-diff-mod (previous step)

m = n0 + m % n ⊦ n = 0, m / n * n = n0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ n ≠ 0 → m % n = m - m / n * n

Rule argument

spec: nat-div inst: name: mod-rew seq: ⊦ n ≠ 0 → m % n = m - m / n * n subst: [n, m] → [n, m] flags: rewrite

Additional information

[Concretesimprules((Csimpnamedseq(nat-div,,cond,n ≠ 0 ⊦ m / n * n ≤ m) Csimpnamedseq(nat-mult,,mult-a, ⊦ m0 * m * n = (m0 * m) * n) Csimpnamedseq(nat-mult,,mult-c, ⊦ m * n = n * m) Csimpnamedseq(nat,,eq-02, n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1) Csimpnamedseq(nat-basic2,,eq-01, ⊦ m + n = m + n0 ↔ n = n0) Csimpnamedseq(nat-basic2,,a, ⊦ (m + n0) + n1 = m + n0 + n1) Csimpnamedseq(nat-basic2,,c, ⊦ m + n = n + m))), Extraterms((nm))]