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Proof step 11 from proof Shor-algorithm (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
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 | abs(i ^ (i0 / 2) - 1) * abs(i ^ (i0 / 2) + 1) ⊦ prime(j), j | i ^ (i0 / 2) + 1

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%abs-eqall: ⊦ abs(i * j) = abs(i) * abs(j); from specification int-mult%sub-zero-01: ⊦ i - 0 = i; from specification int-abs