reserve X for ARS, a,b,c,u,v,w,x,y,z for Element of X;
reserve i,j,k for Element of ARS_01;
reserve l,m,n for Element of ARS_02;
reserve A for set;

theorem
  X is DIAMOND & x <=01= y & y =*=> z implies
  ex u st x =*=> u & u <=01= z
  proof
    assume X is DIAMOND & x <=01= y & y =*=> z; then
    ex u st z =01=> u & u <=*= x by LemA;
    hence thesis;
  end;
