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Proof step 109 from proof Lagrange-SumOf4Squares-primes (previous step)

i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ~1 ≤ j0, ≡mod(0, i, j0), 1 < j, 0 < j, 0 < j0, prime(j), j0 < j, ≡mod(0, i2, j0), ≡mod(0, i1, j0), ≡mod(0, i0, j0), 0 ≤ j, ∀ i3, i4, i5, i6, j1. 0 < j1 ∧ j1 < j0 → i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 ≠ j1 * j ⊦ j = 2, j0 = 1, even(j0)

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: four-square-mod-zero seq: i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(0, i, j0), ≡mod(0, i1, j0), ≡mod(0, i0, j0), ≡mod(0, i2, j0), prime(j), j0 < j, 1 < j, 0 < j, 0 < j0, 0 ≤ j, j ≠ 2, j0 ≠ 1 ⊦ subst: [i2, i1, i0, i, j0, j] → [i2, i1, i0, i, j0, j] flags: current, []

Additional information

Used terms: i2, i1, i0, i, j0, j