reserve V for RealLinearSpace;
reserve p,q,r,u,v,w,y,u1,v1,w1 for Element of V;
reserve a,b,c,d,a1,b1,c1,a2,b2,c2,a3,b3,e,f for Real;
reserve x,y,z for object;
reserve V for non trivial RealLinearSpace;
reserve p,q,r,u,v,w for Element of V;

theorem
  for V holds (the carrier of ProjectiveSpace(V)) = ProjectivePoints(V)
  & (the Collinearity of ProjectiveSpace(V)) = ProjectiveCollinearity(V);
