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Proof step 24 from proof cong-crt-01 (previous step)

j0 * i1 = j * i2, i ^ i0 = j * i2 + i, 0 ≤ i0, 0 < i, prime(j0), prime(j) ⊦ j = 0, j = j0, j0 | i2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ gcd(i, j) = 1 ∧ i * i0 = j * j0 → i | j0

Rule argument

spec: int-gcd inst: name: coprime-divides seq: ⊦ gcd(i, j) = 1 ∧ i * i0 = j * j0 → i | j0 subst: [i, j, i0, j0] → [j0, j, i1, i2] flags: rewrite

Additional information

Used simplifier rules: gcd-primes: ⊦ prime(i) ∧ prime(j) ∧ i ≠ j → gcd(i, j) = 1; from specification int-gcd Used terms: j0, j, i1, i2