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Proof step 17 from proof Shor-algorithm (previous step)

¬ i ^ (i0 / 2) + 1 < 0, 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 | (i ^ (i0 / 2) - 1) * (i ^ (i0 / 2) + 1) ⊦ prime(j), j | i ^ (i0 / 2) + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
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 | (i ^ (i0 / 2) - 1) * (i ^ (i0 / 2) + 1), ~1 ≤ i ^ (i0 / 2) ⊦ prime(j), j | i ^ (i0 / 2) + 1

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; from specification int-abs