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Proof step 132 from proof euler-four-square-identity (previous step)

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

User applied rule simplifier

And obtained the following new goals

Proof step 133:
⊦ 2 * (i4 * j2) * i1 * j3 + 2 * (i3 * j1) * i1 * j3 + 2 * (i3 * j3) * i4 * j4 + 2 * (i1 * j2) * i2 * j1 + 2 * (i4 * j1) * (i1 * j4 + i2 * j3) = 2 * (i1 * j1) * ((i2 * j2 + i3 * j3) + i4 * j4) + 2 * ((i1 * j2 + i2 * j1) + i3 * j4) * i4 * j3

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% ⊦ i + j = i + i0 ↔ j = i0; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult