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Proof step 17 from proof gcd-mod-one (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: nat-mult inst: name: modeq seq: ⊦ n0 < n ∧ n1 < n → (m * n + n0 = m0 * n + n1 ↔ m = m0 ∧ n0 = n1) subst: [n0, n, n1, m, m0] → [n1, n, 1, m1, n0 * m - n0] flags:

Additional information

Used simplifier rules: one: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); from specification nat-basic1%f: ⊦ m < n → n ≠ 0; from specification nat-basic1%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: n1, n, 1, m1, n0 * m - n0