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Proof step 33 from proof Shor-algorithm (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
gcd(i ^ (i0 / 2) - 1, j) = 1, gcd(i, j) = 1, i0 % 2 = 1, 0 < i, 0 < j, even(i0), ≡mod(i ^ i0, 1, j), i < j, 1 < i, 1 < j, 0 < i0 ⊦ i0 = 0, ≡mod(i ^ (2 * i0 / 2) - 1, 0, j), prime(j), ≡mod(i ^ (i0 / 2), ~1, j)

Rule argument

Additional information

Used simplifier rules: numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs