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Proof step 2 from proof mod-crt (previous step)

≡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 lemma

And obtained the following new goals

Proof step 3:
≡mod(i ^ i0, i, j), ≡mod(i ^ i0, i, j0), prime(j), prime(j0), 0 < i, j ≠ j0, 0 ≤ i0 ⊦ ≡mod(i ^ i0, i, j * j0)
Proof step 4:
≡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: cong-crt-01 seq: ≡mod(i ^ i0, i, j), ≡mod(i ^ i0, i, j0), prime(j), prime(j0), 0 < i, j ≠ j0, 0 ≤ i0 ⊦ ≡mod(i ^ i0, i, j * j0) subst: [i, i0, j, j0] → [i, i0, j, j0] flags: current, []

Additional information

Used terms: i, i0, j, j0