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Proof step 3 from proof mod-succ-01 (previous step)

⊦ (m + 1) % n = m % n + 1, m % n + 1 = n, n = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n
Proof step 5:
m = m0 * n + n0, n0 < n ⊦ (m + 1) % n = n0 + 1, n0 + 1 = n, n = 0

Rule argument

spec: <toplevel> 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: <rotated> <all paths>

Additional information

Used terms: m, n, m0, n0