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Proof step 22 from proof gcdnex-prime (previous step)

n0 * m1 | m, 2 ≤ m1, prime(m1), m1 ≤ n0, 2 ≤ n0 ⊦ m = 1, (n0 * m1) * n = 1, m1 = 0, n0 * m1 = 1, n0 = 0, m1 = 1, m1 | m

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-prime inst: name: Divides seq: ⊦ m | n ↔ (∃ n0. m * n0 = n) subst: [n, m] → [m, n0 * m1] flags: rewrite, current

Additional information

Used simplifier rules: divi-mult: ⊦ m | m * n0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: m, n0 * m1