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Proof step 14 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), 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

User applied rule cut formula

And obtained the following new goals

Proof step 15:
0 < j0 / 2 ∧ j0 / 2 < j0, 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

fma: 0 < j0 / 2 ∧ j0 / 2 < j0

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%div-lezero: ⊦ 0 < j → (i / j ≤ 0 ↔ i < j); from specification int-div%two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1%div2-nle: ⊦ 0 < i → ¬ i ≤ i / 2; from specification int-div Used formulas: 0 < j0 / 2 ∧ j0 / 2 < j0