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Proof step 16 from proof Lagrange-SumOf4Squares-primes (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ even(i) ↔ (∃ j. i = j + j)
Proof step 18:
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), ∃ j. j0 = j + j, 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

spec: int-min inst: name: even-def seq: ⊦ even(i) ↔ (∃ j. i = j + j) subst: [i] → [j0] flags: rewrite

Additional information

Used terms: j0