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Proof step 6 from proof mod-crt (previous step)

¬ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
j * j0 < i, j * j0 ≤ 0, 0 ≤ i0, 0 < i, prime(j0), prime(j), ≡mod(i ^ i0, i, j0), ≡mod(i ^ i0, i, j), ≡mod(i ^ i0, i, j * j0) ⊦ j = j0, i ^ i0 |%| (j * j0) = i |%| (j * j0)

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs