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Proof step 2 from proof two-loup-11 (previous step)

m < n, (m + n) / 2 ≤ m, m + 1 < n, (m + n) / 2 < n ⊦ m + 1 = n, 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 + n = m0 * 2 + n0 ∧ n0 < 2 ∧ 2 ≠ 0, m < n, m0 ≤ m, m + 1 < n, m0 < n ⊦ m + 1 = n, 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, 2, m0, n0] flags: rewrite, current

Additional information

Used terms: m + n, 2, m0, n0