proposition: Lemma cpr_eq_pairACr a b c d : `Pr[ TX = a | [% TY, TZ, TW] = (b, c, d) ] = `Pr[ TX = a | [% TY, TW, TZ] = (b, d, c) ].
proof: Proof. rewrite 2!cpr_eqE; congr (_ / _). rewrite !pr_eqE; congr Pr. apply/setP => u; rewrite !inE !xpair_eqE -!andbA; congr (_ && _). by rewrite !andbA andbAC. by rewrite pr_eq_pairAC. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum matrix) mathcomp(Rstruct reals) Reals Lra ssrR Reals_ext realType_ext logb ssr_ext ssralg_ext bigop_ext fdist