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 Th27:
  A is being_line implies a*A is being_line
proof
  set M = a*A;
  assume A is being_line;
  then A // M by Def3;
  hence thesis by AFF_1:36;
end;
