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Proof step 26 from proof lagrange-lemma (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
0 ≤ j0, j1 ≤ (j - 1) / 2, j0 ≤ (j - 1) / 2, prime(j), 0 ≤ j, 0 ≤ j1, j | ~1 - j1 ^2 + j0 ^2, 0 < j ⊦ j = 2, ∃ i, i0, j0. 1 + i ^2 + i0 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%div-abs-02: ⊦ i | abs(j) ↔ i | j; from specification int-gcd%sub-sub: ⊦ i - j - i0 = i - j + i0; from specification int-abs