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Proof step 9 from proof Lagrange-SumOf4Squares (previous step)

Π all_prime_divisors(j) = j, 0 < j ⊦ ∀ j0. j0 ∈ all_prime_divisors(j) → (∃ i, i0, i1, i2. j0 = i ^2 + i0 ^2 + i1 ^2 + i2 ^2), 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 10:
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

Rule argument

Additional information

Used simplifier rules: lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%all_prime_divisors-in-01: ⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i; from specification intlist