(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
Local Open Scope R_scope.
Fixpoint MaxRlist (l:list R) : R :=
match l with
| nil => 0
| a :: l1 =>
match l1 with
| nil => a
| a' :: l2 => Rmax a (MaxRlist l1)
end
end.
Fixpoint MinRlist (l:list R) : R :=
match l with
| nil => 1
| a :: l1 =>
match l1 with
| nil => a
| a' :: l2 => Rmin a (MinRlist l1)
end
end.

Lemma MinRlist_P2 :
forall l:list R, (forall y:R, In y l -> 0 < y) -> 0 < MinRlist l.