proposition: Lemma cdiv1_is_div (c : C) (Hc : (fdistX PQR)`1 c != 0) (Hc1 : (fdistX (fdist_proj13 PQR))`1 c != 0) (Hc2 : (fdistX (fdist_proj23 PQR))`1 c != 0) : cdiv1 c = D((fdistX PQR) `(| c ) || ((fdistX (fdist_proj13 PQR)) `(| c )) `x ((fdistX (fdist_proj23 PQR)) `(| c ))).
proof: Proof. rewrite /cdiv1 /div; apply eq_bigr => -[a b] /= _; rewrite jfdist_condE //. rewrite fdistXI. have [->|H0] := eqVneq (\Pr_PQR[[set (a, b)]|[set c]]) 0; first by rewrite !mul0R. by rewrite fdist_prodE /= jfdist_condE // jfdist_condE // !fdistXI. 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