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Proof step 2 from proof fermat-for-rsa (previous step)

0 ≤ i0, 0 ≤ i, 0 < j, 2 < j, j - 1 | i0, prime(j) ⊦ (i ^ i0 * i) |%| j = i |%| j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 4:
0 ≤ i0, 0 ≤ i, 0 < j, 2 < j, ∃ i1. (j - 1) * i1 = i0, prime(j) ⊦ (i ^ i0 * i) |%| j = i |%| j

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i0, j - 1] flags: rewrite

Additional information

Used terms: i0, j - 1