theorem :: ANPROJ10:71

for V being RealLinearSpace
for P, Q, R, S being Element of V
for x being Tuple of 4, the carrier of V st x = <*P,Q,R,S*> & P,Q,R,S are_mutually_distinct & P,Q,R,S are_collinear holds
ex r being non zero non unit Real st
( r = cross-ratio-tuple x & cross-ratio-tuple (pi_1243 x) = op1 r )