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Proof step 12 from proof Lagrange-SumOf4Squares-primes (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
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

Proof step 12 from proof Lagrange-SumOf4Squares-primes (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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