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Proof step 31 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 * i6)^2 + 2 * (j0 * i6) * i2 + i2 ^2) + (j0 * i3 + i1)^2 + (j0 * i7 + i0)^2 + (j0 * i5 + i)^2 ⊦ j0 = 1, j = 2, j0 | ((j0 * i6)^2 + 2 * (j0 * i6) * i2 + i2 ^2) + (j0 * i3 + i1)^2 + (j0 * i7 + i0)^2 + (j0 * i5 + i)^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, 1 < j, 0 < j, 0 < j0, 0 < ((j0 * i6)^2 + 2 * (j0 * i6) * i2 + i2 ^2) + (j0 * i3 + i1)^2 + (j0 * i7 + i0)^2 + (j0 * i5 + i)^2 ⊦ j0 = 1, j = 2, j0 | (j0 * i6)^2 + i2 ^2 + (j0 * i3 + i1)^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%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%divides-mult-add: ⊦ i | i * j + j0 ↔ i | j0; from specification int-gcd