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Proof step 13 from proof Lagrange-SumOf4Squares-primes (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 14:
i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, i6 ^2 + i5 ^2 + i4 ^2 + i3 ^2 = j0 * j, 1 < j, 0 < j, 0 < j0, prime(j), j0 < j, even(j0), even(i4 + i3), even(i6 + i5), 0 < j0 / 2 ∧ j0 / 2 < j0 → ((i4 - i3) / 2)^2 + ((i4 + i3) / 2)^2 + ((i6 - i5) / 2)^2 + ((i6 + i5) / 2)^2 ≠ j0 / 2 * j ⊦ j = 2, j0 = 1

Rule argument

pos: left 11 terms: (i4 - i3) / 2, (i4 + i3) / 2, (i6 - i5) / 2, (i6 + i5) / 2, j0 / 2 abort: F discard: T computed: F

Additional information

Used terms: (i4 - i3) / 2, (i4 + i3) / 2, (i6 - i5) / 2, (i6 + i5) / 2, j0 / 2