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Proof step 1 from proof cong-crt-01 (conclusion)

≡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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
≡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)

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs