theorem Th2:
  a<>b & a,b,c are_collinear & a,b,d are_collinear implies a,c,d are_collinear
proof
A1: a,b,a are_collinear by ANPROJ_2:def 7;
  assume a<>b & a,b,c are_collinear & a,b,d are_collinear;
  hence thesis by A1,ANPROJ_2:def 8;
end;
