Section limit_laws.
Variable l_diese : forall c : C, Cone c F -> (c --> lim).
Definition Limit_eq (c : C) (tau : Cone c F) (g : c --> lim) :=
forall i : J, g o nu i =_S tau i.
Definition Limit_law1 :=
forall (c : C) (tau : Cone c F), Limit_eq tau (l_diese tau).
Definition Limit_law2 :=
forall (c : C) (tau : Cone c F) (g : c --> lim),
Limit_eq tau g -> g =_S l_diese tau.
End limit_laws.
Structure IsLimit : Type :=
{Lim_diese : forall c : C, Cone c F -> (c --> lim);
Prf_limit1 : Limit_law1 Lim_diese;
Prf_limit2 : Limit_law2 Lim_diese}.
Variable l : IsLimit.

Lemma Ldiese_map :
forall (c : C) (tau1 tau2 : Cone c F),
tau1 =_NT tau2 -> Lim_diese l tau1 =_S Lim_diese l tau2.