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Proof step 87 from proof euler-four-square-identity2 (previous step)

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

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: [j0, j, i] → [(i2 * j2) * i4 * j4, (i2 * j2) * i3 * j3, 2] flags: rewrite

Additional information

Used simplifier rules: numeq: ⊦ (* i2) * i + j = (* i1) * i + j0 ↔ (i2 - i1) * i + j = j0; from specification int-mult%zero-left: ⊦ 0 * i = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%eq-dist: ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0; from specification int-mult Used terms: (i2 * j2) * i4 * j4, (i2 * j2) * i3 * j3, 2