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Proof step 8 from proof cong-crt-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0)
Proof step 10:
prime(j), prime(j0), 0 < i, 0 ≤ i0, j | abs(i ^ i0 - i), j0 | i ^ i0 - i ⊦ j = j0, j * j0 | i ^ i0 - i

Rule argument

spec: int-mod inst: name: congmod-def seq: ⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0) subst: [j, i0, i] → [j, i, i ^ i0] flags: rewrite, current

Additional information

Used terms: j, i, i ^ i0