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) & (a,b // N or b,a // N) & a<>b implies M // N
proof
  assume that
A1: ( a,b // M or b,a // M)&( a,b // N or b,a // N) and
A2: a<>b;
  a,b // M & a,b // N by A1,AFF_1:34;
  hence thesis by A2,AFF_1:53;
end;
