proposition: Lemma nth_cat_ord [T : Type] (x0 : T) (s1 s2 : seq T) (i: 'I_(size s1 + size s2)) : nth x0 (s1 ++ s2) i = match split i with inl i=> nth x0 s1 i | inr i=> nth x0 s2 i end.
proof: Proof. by move: (nth_cat x0 s1 s2 i)=>->; rewrite /split; case: (ltnP i (size s1)). Qed.
imports: Reals mathcomp(all_ssreflect all_algebra vector reals classical_sets Rstruct) infotheo(convex)