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Theorem ex-modeq-half-all

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: Lagrange-SumOf4Squares-primes,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 9
Used lemmas: ex-modeq-half,
Used spec theorems:
- Used simplifier rules:
  - int-abs/forward-le-05