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 Th7:
  ex b9 st a9<>b9
proof
  consider p9,q9,r9 such that
A1: p9<>q9 and
  q9<>r9 and
  r9<>p9 by Th6;
  a9<>p9 or a9<>q9 by A1;
  hence thesis;
end;
