theorem Th4:
  a,b,c are_collinear implies b,a,c are_collinear & a,c,b are_collinear
proof
  assume
A1: a,b,c are_collinear;
  then a=b or a<>b & a,b,b are_collinear & a,b,a are_collinear & a,b,c
  are_collinear by Th2;
  hence b,a,c are_collinear by Th2,Th3;
  a=b or a<>b & a,b,a are_collinear & a,b,c are_collinear & a,b,b
  are_collinear by A1,Th2;
  hence a,c,b are_collinear by Th2,Th3;
end;
