End Sigf.
(*======================================================== GENERAL PROPERTIES OF ORBITS WRT A BIJECTION f: =========================================================*)
(* FUNCTOR : *)
Module Mf(M:Sigf)<:Sigf
with Definition f:=M.f
with Definition f_1:=M.f_1.
Definition f:=M.f.
Definition f_1:=M.f_1.
Definition exd_f:=M.exd_f.
Definition exd_f_1:=M.exd_f_1.
Definition bij_f:=M.bij_f.
Definition bij_f_1:=M.bij_f_1.
Definition f_1_f:=M.f_1_f.
Definition f_f_1:=M.f_f_1.

(* Specifications: *)
Lemma exd_Iter_f:forall(m:fmap)(n:nat)(z:dart),
inv_hmap m -> (exd m z <-> exd m (Iter (f m) n z)).
Lemma exd_Iter_f_1:forall(m:fmap)(n:nat)(z:dart),
inv_hmap m -> (exd m z <-> exd m (Iter (f_1 m) n z)).