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Proof step 9 from proof gcd-mod-one (previous step)

m * m0 + 1 = n * n0, gcd(m, n) = 1, m0 ≤ n * n0 ⊦ m = 0, n = 1, n = 0, (m * (n * n0 - m0)) % n = 1

User applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
m * (n * n0 - m0) = m1 * n + n1 ∧ n1 < n, m * m0 + 1 = n * n0, gcd(m, n) = 1, m0 ≤ n * n0 ⊦ m = 0, n = 1, n = 0, n1 = 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] → [m * (n * n0 - m0), n, m1, n1] flags:

Additional information

Used simplifier rules: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: m * (n * n0 - m0), n, m1, n1