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Proof step 24 from proof lagrange-lemma (previous step)

0 < j, ≡mod(~1 - j1 ^2, j0 ^2, j), 0 ≤ j0, j1 ≤ (j - 1) / 2, j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j, 0 ≤ j1 ⊦ 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 25:
⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0)
Proof step 26:
0 < j, j | abs(~1 - j1 ^2 - j0 ^2), 0 ≤ j0, j1 ≤ (j - 1) / 2, j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j, 0 ≤ j1 ⊦ j = 2, ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j

Rule argument

spec: inst: name: congmod-def seq: ⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0) subst: [j, i0, i] → [j, j0 ^2, ~1 - j1 ^2] flags: rewrite, current

Additional information

Used terms: j, j0 ^2, ~1 - j1 ^2