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Proof step 7 from proof four-square-mod-zero (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(0, i0, j0), ≡mod(0, i2, j0), prime(j), j0 < j, 1 < j, 0 < j, 0 < j0, 0 ≤ j, j0 | i, j0 | i1 ⊦ j0 = 1, j = 2

Rule argument

Additional information

Used simplifier rules: div-abs-02: ⊦ i | abs(j) ↔ i | j; from specification int-gcd%abs-neg: ⊦ abs(~ i) = abs(i); from specification int-abs%neg-06: ⊦ 0 - i = ~ i; from specification int-abs