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

theorem Lem5:
  x ==> y & y =*=> z implies x =*=> z
  proof
    assume
A1: x ==> y;
    assume
A2: y =*=> z;
A3: x =*=> y by A1,Th2;
    thus x =*=> z by A3,A2,Th3;
  end;
