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Local Open Scope R_scope.
(** * Preliminaries lemmas *)
(* end hide *)
(** Intermediate Value Theorem on an Interval (Proof mainly taken from Reals.Rsqrt_def) and its corollary *)

Lemma IVT_interv_prelim1 : forall (x y x0:R) (D : R -> bool),
x < y ->
Un_cv (dicho_up x y D) x0 ->
x <= x0 <= y.