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Proof step 15 from proof Lagrange-SumOf4Squares-primes (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
i6 ^2 + i5 ^2 + i4 ^2 + i3 ^2 = j0 * j, i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, j0 / 2 < j, 0 < j0, 1 < j0, 0 < j0 / 2, even(i6 + i5), even(i4 + i3), even(j0), j0 < j, prime(j), 0 < j, j0 / 2 < j0, 1 < j ⊦ ((i4 - i3) / 2)^2 + ((i4 + i3) / 2)^2 + ((i6 - i5) / 2)^2 + ((i6 + i5) / 2)^2 = j0 / 2 * j, j0 = 1, j = 2

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]