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Proof step 19 from proof Lagrange-SumOf4Squares-primes (previous step)

i6 ^2 + i5 ^2 + i4 ^2 + i3 ^2 = (2 * j1) * j, i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = (2 * j1) * j, prime(j), 0 < j, 1 < j, j1 < j, even(i6 + i5), even(i4 + i3), 2 * j1 < j, 0 < j1 ⊦ j = 2, ((i4 - i3) / 2)^2 + ((i4 + i3) / 2)^2 + ((i6 - i5) / 2)^2 + ((i6 + i5) / 2)^2 = j1 * j

User applied rule cut formula

And obtained the following new goals

Proof step 20:
i6 ^2 + i5 ^2 + i4 ^2 + i3 ^2 = (i6 ^2 + i5 ^2) + i4 ^2 + i3 ^2, i6 ^2 + i5 ^2 + i4 ^2 + i3 ^2 = (2 * j1) * j, i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = (2 * j1) * j, prime(j), 0 < j, 1 < j, j1 < j, even(i6 + i5), even(i4 + i3), 2 * j1 < j, 0 < j1 ⊦ j = 2, ((i4 - i3) / 2)^2 + ((i4 + i3) / 2)^2 + ((i6 - i5) / 2)^2 + ((i6 + i5) / 2)^2 = j1 * j

Rule argument

fma: i6 ^2 + i5 ^2 + i4 ^2 + i3 ^2 = (i6 ^2 + i5 ^2) + i4 ^2 + i3 ^2

Additional information

Used simplifier rules: add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: i6 ^2 + i5 ^2 + i4 ^2 + i3 ^2 = (i6 ^2 + i5 ^2) + i4 ^2 + i3 ^2