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Proof step 22 from proof Shor-algorithm (previous step)

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) * (i ^ (i0 / 2) - 1) + 1 * (i ^ (i0 / 2) - 1), 0, j), ≡mod(i ^ (i0 / 2), ~1, j), prime(j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
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), ≡mod(i ^ (i0 / 2) * (i ^ (i0 / 2) - 1) + i ^ (i0 / 2) - 1, 0, j)

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult