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
( cross-ratio-tuple (pi_3124 x) = 1 / (1 - (cross-ratio-tuple x)) & cross-ratio-tuple (pi_2431 x) = 1 / (1 - (cross-ratio-tuple x)) & cross-ratio-tuple (pi_1342 x) = 1 / (1 - (cross-ratio-tuple x)) & cross-ratio-tuple (pi_4213 x) = 1 / (1 - (cross-ratio-tuple x)) )