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Proof step 5 from proof mod-eq-01 (previous step)

((m1 * n + n0) + m0) % n = m0, m0 < n, n0 < n ⊦ n = 0, n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
n ≠ 0 ⊦ (m + n0 * n) % n = m % n
Proof step 7:
n ≠ 0, (m0 + n0) % n = m0, m0 < n, n0 < n ⊦ n = 0, n0 = 0

Rule argument

spec: nat-div inst: name: mod-mult seq: n ≠ 0 ⊦ (m + n0 * n) % n = m % n subst: [m, n, n0] → [m0 + n0, n, m1] 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: m0 + n0, n, m1