theorem Th6:
  a<>b & a,b,c are_collinear & a,b,d are_collinear implies a,c,d are_collinear
proof
  assume
A1: a<>b & a,b,c are_collinear & a,b,d are_collinear;
  a,b,a are_collinear by Th2;
  hence thesis by A1,Th3;
end;
