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Proof step 2 from proof mod-eq-01 (previous step)

(m + m0) % n = m0, m0 < n ⊦ m % n = 0, n = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n
Proof step 4:
m = m1 * n + n0 ∧ n0 < n, (m + m0) % n = m0, m0 < n ⊦ n0 = 0, n = 0

Rule argument

spec: nat-div inst: name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [m, n, m1, n0] flags: rewrite, current

Additional information

Used terms: m, n, m1, n0