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Proof step 12 from proof gcd-mod-one (previous step)

m * (n * n0 - m0) = m1 * n + n1, m * m0 + 1 = n * n0, gcd(m, n) = 1, n1 < n, m0 ≤ n * n0 ⊦ m = 0, n = 1, n1 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ m0 ≤ m → (m - m0) * n = m * n - m0 * n
Proof step 14:
m * m0 + 1 = n * n0, (n * n0) * m - m0 * m = m1 * n + n1, gcd(m, n) = 1, n1 < n, m0 ≤ n * n0 ⊦ m = 0, n = 1, n1 = 1

Rule argument

spec: nat-mult name: dist-sub seq: ⊦ m0 ≤ m → (m - m0) * n = m * n - m0 * n subst: [n, m0, m] → [m, m0, n * n0] flags: <all paths>

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: m, m0, n * n0