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Proof step 1 from proof four-square-congmod (conclusion)

i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(i3, i2, j0), ≡mod(i4, i1, j0), ≡mod(i5, i0, j0), ≡mod(i6, i, j0), 1 < j, 0 < j, 0 < j0, j ≠ 2, j0 ≠ 1, 0 < i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 ⊦ ≡mod(i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2, 0, j0)

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(i3, i2, j0), ≡mod(i4, i1, j0), ≡mod(i5, i0, j0), ≡mod(i6, i, j0), 1 < j, 0 < j, 0 < j0, 0 < i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 ⊦ j0 = 1, j = 2, ≡mod(i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2, 0, j0)

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