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Proof step 1 from proof four-square-mod-zero (conclusion)

i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(0, i, j0), ≡mod(0, i1, j0), ≡mod(0, i0, j0), ≡mod(0, i2, j0), prime(j), j0 < j, 1 < j, 0 < j, 0 < j0, 0 ≤ j, j ≠ 2, j0 ≠ 1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(0, i, j0), ≡mod(0, i1, j0), ≡mod(0, i0, j0), ≡mod(0, i2, j0), prime(j), j0 < j, 1 < j, 0 < j, 0 < j0, 0 ≤ j ⊦ j0 = 1, j = 2

Rule argument

Additional information

Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs