Require Export Reals Qreals.
Open Scope R_scope.
Local Lemma archimed_1
: forall r : R, r < IZR (up r).
Local Notation " ' x " := (Zpos x) (at level 20, no associativity) : Z_scope.

Lemma rationals_dense_in_reals: forall x y:R, x<y ->
exists q:Q, x < Q2R q < y.