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Proof step 4 from proof Shor-algorithm (previous step)

¬ gcd(i ^ (i0 / 2) - 1, j) ≠ 1, gcd(i, j) = 1, gcd(i ^ (i0 / 2) - 1, j) < i, gcd(i ^ (i0 / 2) - 1, j) < j, 0 ≤ i0, 0 < i, 1 < i, 0 < j, 1 < j, gcd(i ^ (i0 / 2) - 1, j) ≤ 1, even(i0), ≡mod(i ^ i0, 1, j), i < j ⊦ prime(j), ≡mod(i ^ (i0 / 2), ~1, j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
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 ⊦ ≡mod(i ^ (i0 / 2), ~1, j), prime(j)

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs