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Proof step 3 from proof two-loup-05 (previous step)

(m + n) / 2 + 1 < n, (m + n) / 2 + 1 < m, m < n, 2 + (m + n) / 2 < n ⊦

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 + n = m0 * 2 + n0, 2 + m0 < n, m < n, m0 + 1 < m, m0 + 1 < n, n0 < 2 ⊦ 2 = 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, 2, m0, n0] flags: <rotated> <all paths>

Additional information

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