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 ==> y & z ==> y implies x >>01<< z
  proof
    assume
A1: x ==> y;
    assume
A2: z ==> y;
    take y;
    thus y <=01= x by A1;
    thus z =01=> y by A2;
  end;
