proposition: Lemma scaleR_addpt : {morph scaleR : x y / addpt x y >-> (x + y)%coqR}.
proof: Proof. move=> [p x|] [q y|] /=; rewrite ?(add0R,addR0) //. rewrite avgRE /avg /divRposxxy /= RdivE' onem_div /Rdiv; last exact: Rpos_neq0. rewrite -!RmultE -!RinvE' -!(mulRC (/ _)%coqR) mulRDr !mulRA mulRV; last exact: Rpos_neq0. by rewrite !mul1R (addRC p) addrK. 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