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Proof step 40 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 ⊦ prime(j), ≡mod(i ^ (i0 / 2), ~1, j), j | i ^ i0 - 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: congmod-def seq: ⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0) subst: [j, i0, i] → [j, 1, i ^ i0] flags: rewrite, current

Additional information

Used simplifier rules: div-abs-02: ⊦ i | abs(j) ↔ i | j; from specification int-gcd Used terms: j, 1, i ^ i0