proposition: Lemma varianceD_cst_r (X : {RV P >-> R}) c : P.-integrable setT (EFin \o X) -> P.-integrable setT (EFin \o (X ^+ 2)%R) -> 'V_P[(X \+ cst c)%R] = 'V_P[X].
proof: Proof. move=> X1 X2. have -> : (X \+ cst c = cst c \+ X)%R by apply/funeqP => x /=; rewrite addrC. exact: varianceD_cst_l. Qed.
imports: mathcomp(all_ssreflect) mathcomp(ssralg poly ssrnum ssrint interval finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality) HB(structures) exp numfun lebesgue_measure lebesgue_integral reals ereal signed topology normedtype sequences esum measure exp numfun lebesgue_measure lebesgue_integral