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Proof step 70 from proof euler-four-square-identity (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 71:
⊦ i * (j + j0) = i * j + i * j0
Proof step 72:
⊦ 2 * (i3 * j1) * i1 * j3 + 2 * (i3 * j3) * i4 * j4 + 2 * (i2 * j1) * i3 * j4 + 2 * (i4 * j1) * (i1 * j4 + i2 * j3) + 2 * (i1 * j4) * i2 * j3 = ((i1 * j1) * i3 * j3 + (i1 * j1) * i4 * j4) * 2 + ((j4 * i2 * 2) * i1 * j3 + (j4 * i2 * 2) * i3 * j1) + (j3 * i4 * 2) * (i3 * j4 + i2 * j1)

Rule argument

spec: int-mult inst: name: dist-rsplit seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [i3 * j1, i1 * j3, j4 * i2 * 2] flags: rewrite

Additional information

Used terms: i3 * j1, i1 * j3, j4 * i2 * 2