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Proof step 131 from proof euler-four-square-identity2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 132:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 133:
⊦ 2 * (i1 * j1) * i4 * j4 + 2 * (i2 * j2) * i3 * j3 + 2 * i1 * j3 * i2 * j4 + 2 * i3 * j1 * i4 * j2 = 2 * ((i3 * j2) * (i2 * j3 + i4 * j1) + (i1 * j4) * (i2 * j3 + i4 * j1))

Rule argument

spec: int-mult name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [i2 * j3 + i4 * j1, i1 * j4, i3 * j2] flags: <all paths>

Additional information

Used terms: i2 * j3 + i4 * j1, i1 * j4, i3 * j2