reserve x,y for set;
reserve X for non empty set;
reserve a,b,c,d for Element of X;
reserve S for OAffinSpace;
reserve a,b,c,d,p,q,r,x,y,z,t,u,w for Element of S;

theorem Th30:
  x,y,z are_collinear implies x,z,y are_collinear & y,x,z
  are_collinear & y,z,x are_collinear & z,x,y are_collinear &
  z,y,x are_collinear
proof
  assume x,y,z are_collinear;
  hence x,z,y are_collinear & y,x,z are_collinear by Lm3;
  hence y,z,x are_collinear & z,x,y are_collinear by Lm3;
  hence thesis by Lm3;
end;
