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
  (a,b // M or b,a // M) & (c,d // M or d,c // M) implies a,b // c,d
proof
  assume ( a,b // M or b,a // M)&( c,d // M or d,c // M);
  then A1: a,b // M & c,d // M by AFF_1:34;
  then M is being_line by AFF_1:26;
  hence thesis by A1,AFF_1:31;
end;
