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

theorem Lem5A:
  x ==> y & y =+=> z implies x =*=> z
  proof
    assume
A1: x ==> y;
    assume
A2: y =+=> z;
A3: x =*=> y by A1,Th2;
A4: y =*=> z by A2,Lem2;
    thus x =*=> z by A3,A4,Th3;
  end;
