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Proof step 30 from proof lagrange-lemma (previous step)

0 < j, 0 ≤ j0, j1 ≤ (j - 1) / 2, j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j, 0 ≤ j1, j | (j1 ^2 + j0 ^2) + 1 ⊦ j = 2, ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 32:
0 < j, 0 ≤ j0, j1 ≤ (j - 1) / 2, j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j, 0 ≤ j1, ∃ i0. j * i0 = (j1 ^2 + j0 ^2) + 1 ⊦ j = 2, ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [(j1 ^2 + j0 ^2) + 1, j] flags: rewrite

Additional information

Used terms: (j1 ^2 + j0 ^2) + 1, j