(** *   Derivability of the reciprocal function        *)

Lemma derivable_pt_lim_recip_interv : forall (f g:R->R) (lb ub x:R)
(Prf:forall a : R, g lb <= a <= g ub -> derivable_pt f a) (Prg : continuity_pt g x),
lb < ub ->
lb < x < ub ->
forall (Prg_incr:g lb <= g x <= g ub),
(forall x, lb <= x <= ub -> (comp f g) x = id x) ->
derive_pt f (g x) (Prf (g x) Prg_incr) <> 0 ->
derivable_pt_lim g x (1 / derive_pt f (g x) (Prf (g x) Prg_incr)).