reserve X for ARS, a,b,c,u,v,w,x,y,z for Element of X;

theorem Lem31:
  x <=01=> y implies x <== y or x = y or x ==> y
  proof
    assume
A1: x <=01=> y;
A2: x <==> y or x = y by A1;
    thus x <== y or x = y or x ==> y by A2;
  end;
