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conditional_divergence
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affeldt-aist committed Apr 21, 2024
1 parent ddb48dd commit 2a71a75
Showing 1 changed file with 8 additions and 3 deletions.
11 changes: 8 additions & 3 deletions information_theory/conditional_divergence.v
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(* 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 finset matrix.
From mathcomp Require Import all_ssreflect ssralg ssrnum finset matrix.
Require Import Reals.
From mathcomp Require Import Rstruct.
From mathcomp Require Import Rstruct reals.
Require Import ssrR realType_ext Reals_ext ssr_ext ssralg_ext logb ln_facts.
Require Import num_occ fdist entropy channel divergence types jtypes.
Require Import proba jfdist_cond.
Expand Down Expand Up @@ -139,7 +139,12 @@ have [H'|H'] := eqVneq ((R `X Q) (a, b)) 0.
by move/eqP : H; tauto.
rewrite -RmultE.
by rewrite !(mulR0,mul0R,div0R).
by rewrite 2!fdist_prod1 /=; field; split; exact/eqP.
rewrite 2!fdist_prod1 /=.
set x := R _.
set y := (R `X P _).
set z := (R `X Q _).
field.
split; exact/eqP.
Qed.

End conditional_divergence_vs_conditional_relative_entropy.
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