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Proof step 141 from proof euler-four-square-identity2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 142:
⊦ i * (j + j0) = i * j + i * j0
Proof step 143:
⊦ 2 * (i1 * j1) * i4 * j4 + 2 * (i2 * j2) * i3 * j3 + 2 * i1 * j3 * i2 * j4 + 2 * i3 * j1 * i4 * j2 = (2 * (i3 * j2) * i2 * j3 + 2 * (i3 * j2) * i4 * j1) + 2 * (i1 * j4) * i2 * j3 + 2 * (i1 * j4) * i4 * j1

Rule argument

spec: int-mult name: dist-rsplit seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [(i1 * j4) * i4 * j1, (i1 * j4) * i2 * j3, 2] flags: <all paths>

Additional information

Used terms: (i1 * j4) * i4 * j1, (i1 * j4) * i2 * j3, 2