theorem Th40: :: ANPROJ10:72

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_collinear & P <> R & P <> S & Q <> R & Q <> S holds
( cross-ratio-tuple (pi_1243 x) = 1 / (cross-ratio-tuple x) & cross-ratio-tuple (pi_2134 x) = 1 / (cross-ratio-tuple x) & cross-ratio-tuple (pi_3421 x) = 1 / (cross-ratio-tuple x) & cross-ratio-tuple (pi_4312 x) = 1 / (cross-ratio-tuple x) )