theorem Th42: :: ANPROJ10:75

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_1423 x) = ((cross-ratio-tuple x) - 1) / (cross-ratio-tuple x) & cross-ratio-tuple (pi_2314 x) = ((cross-ratio-tuple x) - 1) / (cross-ratio-tuple x) & cross-ratio-tuple (pi_4132 x) = ((cross-ratio-tuple x) - 1) / (cross-ratio-tuple x) & cross-ratio-tuple (pi_3241 x) = ((cross-ratio-tuple x) - 1) / (cross-ratio-tuple x) )