reserve CPS for proper CollSp,
  B for Subset of CPS,
  p for Point of CPS,
  x, y, z, Y for set;

theorem Th1:
  x is LINE of CPS iff x is Element of ProjectiveLines(CPS)
proof
  hereby
    assume x is LINE of CPS;
    then x in {B : B is LINE of CPS};
    hence x is Element of ProjectiveLines(CPS);
  end;
  assume x is Element of ProjectiveLines(CPS);
  then x in ProjectiveLines(CPS);
  then ex B st x=B & B is LINE of CPS;
  hence thesis;
end;
