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Proof step 39 from proof Shor-algorithm (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
i0 % 2 = 0, gcd(i ^ (i0 / 2) - 1, j) = 1, gcd(i, j) = 1, 0 < i0, 1 < j, 0 ≤ i0, even(i0), ≡mod(i ^ i0, 1, j), i < j, 1 < i, 0 < i, 0 < j, 2 ≤ i0 ⊦ prime(j), ≡mod(i ^ (i0 / 2), ~1, j), j | i ^ i0 - 1

Rule argument

Additional information

Used simplifier rules: div-abs-02: ⊦ i | abs(j) ↔ i | j; from specification int-gcd%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-sub: ⊦ i - j - i0 = i - j + i0; from specification int-abs