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Proof step 80 from proof euler-four-square-identity2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 81:
⊦ i * (j + j0) = i * j + i * j0
Proof step 82:
⊦ 2 * ((i2 * j2) * i3 * j3 + (i2 * j2) * i4 * j4) + 2 * ((i1 * j1) * i2 * j2 + (i1 * j1) * (i3 * j3 + i4 * j4)) = 2 * (i3 * j2) * i2 * j3 + 2 * (i1 * j4) * i4 * j1 + 2 * (i1 * j3) * i3 * j1 + 2 * (i2 * j4) * i4 * j2 + (i2 * j1) * j2 * i1 * 2

Rule argument

spec: int-mult inst: name: dist-rsplit seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [i4 * j4, i3 * j3, i2 * j2] flags: rewrite

Additional information

Used terms: i4 * j4, i3 * j3, i2 * j2