reserve AS for AffinSpace;
reserve a,b,c,d,a9,b9,c9,d9,p,q,r,x,y for Element of AS;
reserve A,C,K,M,N,P,Q,X,Y,Z for Subset of AS;

theorem
  X is being_plane & Y is being_plane & a in X & a in Y & X '||' Y
  implies X=Y by Lm13;
