reserve AS for AffinSpace;
reserve A,K,M,X,Y,Z,X9,Y9 for Subset of AS;
reserve zz for Element of AS;
reserve x,y for set;

theorem
  X=the carrier of AS & X is being_plane implies AS is AffinPlane
proof
  assume that
A1: X=the carrier of AS and
A2: X is being_plane;
  assume AS is not AffinPlane;
  then ex zz st not zz in X by A2,AFF_4:48;
  hence contradiction by A1;
end;
