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Proof step 6 from proof Lagrange-SumOf4Squares (previous step)

0 < j → 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 7:
Π all_prime_divisors(j) = j, 0 < j ⊦ j = 0, ∃ i, i0, i1, i2. j = i ^2 + i0 ^2 + i1 ^2 + i2 ^2

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs