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Proof step 8 from proof Shor-algorithm (previous step)

≡mod((i ^ (i0 / 2) - 1) * (i ^ (i0 / 2) + 1), 0, j), gcd(i, j) = 1, gcd(i ^ (i0 / 2) - 1, j) = 1, 1 < i, i < j, ≡mod(i ^ i0, 1, j), even(i0), 0 < j, 0 < i, 0 ≤ i0, 1 < j ⊦ j | abs(i ^ (i0 / 2) - ~1), prime(j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
gcd(i, j) = 1, gcd(i ^ (i0 / 2) - 1, j) = 1, ≡mod((i ^ (i0 / 2) - 1) * (i ^ (i0 / 2) + 1), 0, j), 1 < i, i < j, ≡mod(i ^ i0, 1, j), even(i0), 0 < j, 0 < i, 0 ≤ i0, 1 < j ⊦ prime(j), j | i ^ (i0 / 2) + 1

Rule argument

Additional information

Used simplifier rules: div-abs-02: ⊦ i | abs(j) ↔ i | j; from specification int-gcd%minus-neg: j < 0 ⊦ i - (* j) = i + ~ j; from specification int-abs