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fix sumRE #113

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Mar 11, 2024
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2 changes: 1 addition & 1 deletion lib/ssrR.v
Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
(* infotheo: information theory and error-correcting codes in Coq *)
(* Copyright (C) 2020 infotheo authors, license: LGPL-2.1-or-later *)
From mathcomp Require Import all_ssreflect ssralg ssrnum.
Require Import Reals.

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From mathcomp Require Import lra.
From mathcomp Require Import Rstruct.

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Proof. by rewrite -{1}(addR0 x) ltR_add2l. Qed.

Lemma subR_gt0 x y : (0 < y - x) <-> (x < y).
Proof. by split; [exact: Rminus_gt_0_lt | exact: Rlt_Rminus]. Qed.

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Lemma subR_lt0 x y : (y - x < 0) <-> (y < x).
Proof. by split; [exact: Rminus_lt | exact: Rlt_minus]. Qed.
Lemma subR_ge0 x y : (0 <= y - x) <-> (x <= y).
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Local Open Scope ring_scope.

Lemma sumRE (I : Type) (r : seq I) (P : pred I) (F : I -> R) :
\sum_(i <- r | P i) F i = \big[+%R/0]_(i <- r | P i) F i.
(\sum_(i <- r | P i) F i)%coqR = \sum_(i <- r | P i) F i.
Proof. by []. Qed.

Lemma bigmaxRE (I : Type) (r : seq I) (P : pred I) (F : I -> R) :
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