reserve CPS for proper CollSp,
  B for Subset of CPS,
  p for Point of CPS,
  x, y, z, Y for set;
reserve a,b,c,p,q for POINT of IncProjSp_of(CPS),
  P,Q for LINE of IncProjSp_of(CPS),
  a9,b9,c9,p9,q9,r9 for Point of CPS,
  P9 for LINE of CPS;

theorem Th8:
  p on P & q on P & p on Q & q on Q implies p = q or P = Q
proof
  reconsider p9= p, q9= q as Point of CPS;
  reconsider P9= P, Q9= Q as LINE of CPS by Th1;
  assume that
A1: p on P & q on P and
A2: p on Q & q on Q and
A3: p<>q;
A4: p9 in Q9 & q9 in Q9 by A2,Th5;
  p9 in P9 & q9 in P9 by A1,Th5;
  hence thesis by A3,A4,COLLSP:20;
end;
