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Theorem euler-four-square-identity

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 29
Proof steps: 48
Used lemmas: two-mult, two-plus, two-minus,
Used spec theorems:
- int-mult/dist-rsplit
- int-mult/dist-lsplit
Used simplifier rules: