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Proof step 76 from proof euler-four-square-identity (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [j1 * i4, i2 * j3, i1 * j4] flags: rewrite

Additional information

Used simplifier rules: eq-succ-01: ⊦ (i + i0) * j + j0 = (i + i1) * j + j1 ↔ i0 * j + j0 = i1 * j + j1; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j1 * i4, i2 * j3, i1 * j4