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 Th2:
  (a,b // A or b,a // A) & a in A implies b in A
proof
  assume that
A1: a,b // A or b,a // A and
A2: a in A;
  a,b // A & A is being_line by A1,AFF_1:26,34;
  hence thesis by A2,AFF_1:23;
end;
