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Proof step 5 from proof two-ppred (previous step)

n0 < 2 ⊦ m0 = (m0 * 2 + n0 - 2) / 2 + 1, m0 * 2 + n0 = 0, m0 = 0 ∧ n0 = 1

User applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n
Proof step 7:
m0 * 2 + n0 - 2 = m1 * 2 + n1 ∧ n1 < 2 ∧ 2 ≠ 0, n0 < 2 ⊦ m0 = m1 + 1, m0 * 2 + n0 = 0, m0 = 0 ∧ n0 = 1

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] → [m0 * 2 + n0 - 2, 2, m, n] flags: current, []

Additional information

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