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

m * m0 = m1 * n + 1, gcd(m, n) = 1 ⊦ n = 1, n = 0, n * m1 = dist(m * m0, 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-prime inst: name: dist-snd-01 seq: ⊦ n ≤ m → dist(m, n) = m - n subst: [n, m] → [1, m * m0] flags: rewrite, current

Additional information

Used simplifier rules: lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%z-01: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; from specification nat-basic2%zero-06: ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: 1, m * m0