(* The strict order is conserved when injecting Q in R. *)

Lemma Qlt_Rlt : forall a b, a<b -> Rlt (inject_Q a) (inject_Q b).
Record itvl2: Set:= {lft1:Q; rht1:Q; lft2:Q; rht2:Q; lft1_rht1: lft1<rht1; lft2_rht2: lft2<rht2}.