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Proof step 22 from proof euler-four-square-identity (previous step)

⊦ ((i2 * j2 + i3 * j3) + i4 * j4)^2 + (i4 * j3)^2 + (i4 * j2 + i3 * j1 + i1 * j3 - i2 * j4)^2 + (i4 * j1 + i1 * j4 + i2 * j3 - i3 * j2)^2 + (i1 * j2)^2 + 2 * (i1 * j2) * i2 * j1 + 2 * (i1 * j2 + i2 * j1) * i3 * j4 + (i3 * j4)^2 = (i3 ^2 + i4 ^2) * j1 ^2 + (i1 ^2 + i2 ^2 + i3 ^2 + i4 ^2) * (j2 ^2 + j3 ^2 + j4 ^2) + 2 * (i1 * j1) * ((i2 * j2 + i3 * j3) + i4 * j4) + 2 * ((i1 * j2 + i2 * j1) + i3 * j4) * i4 * j3

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [j2 ^2 + j3 ^2 + j4 ^2, i2 ^2 + i3 ^2 + i4 ^2, i1 ^2] flags: <all paths>

Additional information

Used terms: j2 ^2 + j3 ^2 + j4 ^2, i2 ^2 + i3 ^2 + i4 ^2, i1 ^2