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Proof step 60 from proof euler-four-square-identity2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: dist-rsplit seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [i, j0, j] → [(i2 * j1 + i3 * j4) * 2, i1 * j2, i4 * j3] flags: rewrite

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: (i2 * j1 + i3 * j4) * 2, i1 * j2, i4 * j3