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Proof step 34 from proof Shor-algorithm (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-min inst: name: even-def-mod seq: ⊦ even(i) ↔ i % 2 = 0 subst: [i] → [i0] flags: rewrite

Additional information

Used simplifier rules: divmult: j ≠ 0 ⊦ i % j = 0 → i / j * j = i; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista] Used terms: i0