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Proof step 48 from proof four-square-congmod (previous step)

i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, 1 < j, 0 < j, 0 < j0, 0 < (j0 ^2 * i6 ^2 + 2 * (j0 * i6) * i2 + i2 ^2) + (j0 ^2 * i3 ^2 + 2 * (j0 * i3) * i1 + i1 ^2) + (j0 ^2 * i7 ^2 + 2 * (j0 * i7) * i0 + i0 ^2) + (j0 * i5)^2 + 2 * (j0 * i5) * i + i ^2 ⊦ j0 = 1, j = 2, j0 | j0 ^2 * i6 ^2 + i2 ^2 + j0 ^2 * i3 ^2 + i1 ^2 + j0 ^2 * i7 ^2 + i0 ^2 + (j0 * i5)^2 + i ^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, 1 < j, 0 < j, 0 < j0, 0 < (j0 ^2 * i6 ^2 + 2 * (j0 * i6) * i2 + i2 ^2) + (j0 ^2 * i3 ^2 + 2 * (j0 * i3) * i1 + i1 ^2) + (j0 ^2 * i7 ^2 + 2 * (j0 * i7) * i0 + i0 ^2) + (j0 * i5)^2 + 2 * (j0 * i5) * i + i ^2 ⊦ j0 = 1, j = 2, j0 | j0 ^2 * i6 ^2 + i2 ^2 + j0 ^2 * i3 ^2 + i1 ^2 + j0 ^2 * i7 ^2 + i0 ^2 + (j0 * i5)^2 + i ^2

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs