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Proof step 30 from proof Lagrange-SumOf4Squares-primes (previous step)

0 < j0, odd(j0), i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j ⊦ ∃ i3, i4, i5, i6. ≡mod(i3, i, j0) ∧ abs(i3) ≤ j0 / 2 ∧ ≡mod(i4, i0, j0) ∧ abs(i4) ≤ j0 / 2 ∧ ≡mod(i5, i1, j0) ∧ abs(i5) ≤ j0 / 2 ∧ ≡mod(i6, i2, j0) ∧ abs(i6) ≤ j0 / 2

Lemma ex-modeq-half-all