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Proof step 56 from proof euler-four-square-identity2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic2 name: add-c seq: ⊦ i + j = j + i subst: [j, i] → [ i4 ^2 * j2 ^2 + (i2 * j1 + i3 * j4)^2 + (i2 * j3 + i4 * j1)^2 + i4 ^2 * j3 ^2 + 2 * i4 * j3 * i1 * j2 + (((i1 * j1 + i2 * j2) + i3 * j3) + i4 * j4)^2 + (i1 * j3 + i2 * j4)^2 + 2 * i3 * j2 * i1 * j4, 2 * i3 * j1 * i4 * j2] flags: <all paths>

Additional information

Used terms: i4 ^2 * j2 ^2 + (i2 * j1 + i3 * j4)^2 + (i2 * j3 + i4 * j1)^2 + i4 ^2 * j3 ^2 + 2 * i4 * j3 * i1 * j2 + (((i1 * j1 + i2 * j2) + i3 * j3) + i4 * j4)^2 + (i1 * j3 + i2 * j4)^2 + 2 * i3 * j2 * i1 * j4, 2 * i3 * j1 * i4 * j2