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Proof step 2 from proof cong-crt-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0)
Proof step 4:
≡mod(i ^ i0, i, j), ≡mod(i ^ i0, i, j0), prime(j), prime(j0), 0 < i, 0 ≤ i0 ⊦ j = j0, j * j0 | abs(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 * j0, i, i ^ i0] flags: rewrite, current

Additional information

Used terms: j * j0, i, i ^ i0