proposition: Lemma entropy_uniform n (An1 : #|A| = n.+1) : `H (fdist_uniform An1) = log (INR #|A|).
proof: Proof. rewrite /entropy. under eq_bigr do rewrite fdist_uniformE. rewrite big_const iter_addR mulRA RmultE -RinvE; last first. by rewrite An1 -INRE INR_eq0'. rewrite INRE mulRV; last by rewrite An1 -INRE INR_eq0'. rewrite -RmultE mul1R logV ?oppRK//; rewrite An1. by rewrite -INRE; apply/ltR0n. Qed.
imports: mathcomp(all_ssreflect all_algebra fingroup perm matrix) Reals mathcomp(Rstruct) ssrR Reals_ext realType_ext ssr_ext ssralg_ext bigop_ext logb ln_facts fdist jfdist_cond proba binary_entropy_function divergence