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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
⊦ 2 * (i3 * j1) * i1 * j3 + 2 * (i4 * j2) * i1 * j3 + 2 * (i2 * j2) * i4 * j4 + 2 * (i3 * j3) * i4 * j4 + 2 * (i1 * j2) * (i2 * j1 + i3 * j4) + 2 * (i2 * j1) * i3 * j4 + 2 * (i4 * j1) * (i1 * j4 + i2 * j3) + 2 * (i1 * j4) * i2 * j3 = (j2 * i3 * 2) * i1 * j4 + 2 * (i4 * j2 + i3 * j1 + i1 * j3) * i2 * j4 + 2 * ((i1 * j2 + i2 * j1) + i3 * j4) * i4 * j3 + 2 * (i1 * j1) * ((i2 * j2 + i3 * j3) + i4 * j4)

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%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-left: ⊦ 0 * i = 0; from specification int-mult%numeq: ⊦ (* i2) * i + j = (* i1) * i + j0 ↔ (i2 - i1) * i + j = j0; from specification int-mult