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Proof step 2 from proof mod-succ-04 (previous step)

⊦ (m + 1) % n < m % n ↔ (m + 1) % n = 0 ∧ n ≠ 1, n = 0

Heuristic elimination 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 = m0 * n + n0 ∧ n0 < n ⊦ (m + 1) % n < n0 ↔ (m + 1) % n = 0 ∧ n ≠ 1, 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, m0, n0] flags: rewrite, current

Additional information

Used terms: m, n, m0, n0