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

∃ i, i0, i1, i2. Π all_prime_divisors(j) = i ^2 + i0 ^2 + i1 ^2 + i2 ^2, Π all_prime_divisors(j) = j, 0 < j ⊦ j = 0, ∃ i, i0, i1, i2. j = i ^2 + i0 ^2 + i1 ^2 + i2 ^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
Π all_prime_divisors(i2 ^2 + i1 ^2 + i0 ^2 + i ^2) = i2 ^2 + i1 ^2 + i0 ^2 + i ^2, 0 < i2 ^2 + i1 ^2 + i0 ^2 + i ^2 ⊦ i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = 0, ∃ i6, i5, i4, i3. i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = i6 ^2 + i5 ^2 + i4 ^2 + i3 ^2

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs