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Proof step 4 from proof mod-crt (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j)
Proof step 6:
¬ 0 < j * j0, ≡mod(i ^ i0, i, j * j0), ≡mod(i ^ i0, i, j), ≡mod(i ^ i0, i, j0), prime(j), prime(j0), 0 < i, 0 ≤ i0 ⊦ i ^ i0 |%| (j * j0) = i |%| (j * j0), j = j0

Rule argument

spec: int-mod inst: name: congmod-def-mod seq: ⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j) subst: [j, i0, i] → [j * j0, i, i ^ i0] flags: rewrite, current

Additional information

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