The Fundamental Theorem of Inversive Geometry
If L = (α,β,γ) and L' = (α',β',γ') are lists of distinct points of E^{+},


Proof By the (0,1,∞) Theorem, there exist elements r, s of I^{+}(2) such that r maps L to (0,1,∞), and s maps M to (0,1,∞). Then t = s^{1}or maps L to M.
Suppose that u also maps L to M. Then sou maps L to (0,1,∞).
