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Theorem lagrange-lemma-smallest

prime(j), j ≠ 2 ⊦ ∃ i, i0, i1, i2, j0. i ^2 + i0 ^2 + i1 ^2 + i2 ^2 = j0 * j ∧ 0 < j0 ∧ j0 < j ∧ (∀ i3, i4, i5, i6, j1. 0 < j1 ∧ j1 < j0 → i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 ≠ j1 * j)

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: 6
Proof steps: 11
Used lemmas: lagrange-lemma,
Used spec theorems:
- Used simplifier rules:
  - int-abs/forward-le-05
  - int-basic2/add-c
  - int-basic2/add-a
  - int-square/zero-i
  - int-square/one
  - int-basic1/forward-pos
  - oelem/intlista/transitivity
  - intnat/labs
  - int-abs/abs
  - int-abs/abs-16
  - int-abs/lels
  - int-abs/lels-03