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Proof step 11 from proof Lagrange-SumOf4Squares (previous step)

j0 = 2, Π all_prime_divisors(j) = j, 2 ≤ j, j0 | j, prime(j0), 0 < j ⊦ j = 0, ∃ i, i0, i1, i2. j = i ^2 + i0 ^2 + i1 ^2 + i2 ^2, ∃ i, i0, i1, i2. j0 = i ^2 + i0 ^2 + i1 ^2 + i2 ^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
Π all_prime_divisors(j) = j, 2 ≤ j, 2 | j, 0 < j ⊦ j = 0, ∃ i, i0, i1, i2. j = i ^2 + i0 ^2 + i1 ^2 + i2 ^2, ∃ i, i0, i1, i2. 2 = i ^2 + i0 ^2 + i1 ^2 + i2 ^2

Rule argument

Additional information

Used simplifier rules: prime-two-01: ⊦ prime(2); from specification int-gcd