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Proof step 11 from proof cong-crt-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 13:
∃ i1. j0 * i1 = i ^ i0 - i, prime(j), prime(j0), 0 < i, 0 ≤ i0, j | i ^ i0 - i ⊦ j = j0, j * j0 | i ^ i0 - i

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i ^ i0 - i, j0] flags: rewrite

Additional information

Used terms: i ^ i0 - i, j0