reserve X,Y,Z,Z1,Z2,D for set,x,y for object;
reserve SFX,SFY,SFZ for set;
reserve F,G for Subset-Family of D;
reserve P for Subset of D;
reserve E for set;

theorem
  for X being set, F being Subset-Family of X holds F is Cover of X iff
  union F = X
by Def11;
