proposition: Lemma avgr_addD p (a b c d : E) : (a + b) <|p|> (c + d) = (a <|p|> c) + (b <|p|> d).
proof: Proof. rewrite !avgrE !scalerDr !addrA; congr +%R; rewrite -!addrA; congr +%R. exact: addrC. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg fingroup perm matrix) mathcomp(mathcomp_extra boolp classical_sets Rstruct) mathcomp(ssrnum ereal) mathcomp(lra Rstruct reals) Reals ssrR Reals_ext Ranalysis_ext ssr_ext ssralg_ext logb realType_ext fdist