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Proof step 80 from proof Lagrange-SumOf4Squares-primes (previous step)

⊦ j0 ^2 * i11 ^2 + (j0 * i10)^2 + (j0 * i8)^2 + (j0 * i9)^2 = j0 ^2 * i11 ^2 + j0 ^2 * (i10 ^2 + i8 ^2 + i9 ^2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
⊦ (j0 * i10)^2 + (j0 * i8)^2 + (j0 * i9)^2 = j0 ^2 * (i10 ^2 + i8 ^2 + i9 ^2)

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2