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

theorem
  x ==> y & y =+=> z & z ==> u implies x =+=> u
  proof
    assume
A1: x ==> y;
    assume
A2: y =+=> z;
    assume
A3: z ==> u;
A4: x =*=> z by A1,A2,Lem5A;
    thus x =+=> u by A3,A4,Th4;
  end;
