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

theorem LemN:
  x =*=> y implies x = y or x =+=> y
  proof
    assume
A1: x =*=> y;
    defpred P[Element of X] means x = $1 or x =+=> $1;
A2: P[x];
A3: for y,z st y ==> z & P[y] holds P[z]
    proof
      let y,z;
      assume
A4:   y ==> z;
      assume
A5:   P[y];
A6:   x =*=> y by A5,Lem2;
      thus P[z] by A6,A4,Th4;
    end;
    thus P[y] from Star1(A1,A2,A3);
  end;
