proposition: Lemma BQ_of_R_prop x: rationalp x -> x = BR_of_Q (BQ_of_R x) /\ inc (BQ_of_R x) BQ.
proof: Proof. move => /BR_of_Q_prop2 Ha. have Hb:singl_val2 (inc^~ BQ) (fun y => x = BR_of_Q y). by move => u v /= uq eq1 vq; rewrite eq1;apply: BR_of_Q_inj1. exact: (select_pr Ha Hb). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)