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Proof step 22 from proof four-square-congmod (previous step)

i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(i4, i1, j0), 0 < i3 ^2 + i4 ^2 + (j0 * i7 + i0)^2 + (j0 * i5 + i)^2, 1 < j, 0 < j, 0 < j0, ∃ i0. j0 * i0 = i3 - i2 ⊦ j0 = 1, j = 2, j0 | i3 ^2 + i4 ^2 + (j0 * i7 + i0)^2 + (j0 * i5 + i)^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, 0 < j0, 0 < j, 1 < j, ≡mod(i4, i1, j0), 0 < (j0 * i6 + i2)^2 + i4 ^2 + (j0 * i7 + i0)^2 + (j0 * i5 + i)^2 ⊦ j = 2, j0 = 1, j0 | (j0 * i6 + i2)^2 + i4 ^2 + (j0 * i7 + i0)^2 + (j0 * i5 + i)^2

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs