reserve X,Y,Z,Z1,Z2,D for set,x,y for object;
reserve SFX,SFY,SFZ for set;

theorem
  SFX is_finer_than UNION(SFX,SFX)
proof
  let X such that
A1: X in SFX;
  take X;
  X = X \/ X;
  hence thesis by A1,Def4;
end;
