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

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

User applied rule exists right

And closed the goal!

Rule argument

pos: right 3 terms: 0, 0, 1, 1 abort: F discard: T computed: F

Additional information

Used simplifier rules: zero-i: ⊦ 0 ^2 = 0; from specification int-square%one: ⊦ 1 ^2 = 1; from specification int-square%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: 0, 0, 1, 1