proposition: Theorem Rmorph_id (R : Real.model) : Real.morphism (@idfun R).
proof: Proof. split=> //= E supE; set F := Real.image idfun E. have eqEF: pointwise_relation R iff (Real.down E) (Real.down F). by move=> x; split=> [[y Ey] | [_ [y Ey ->]]]; exists y => //; exists y. have supF: Real.has_sup F by rewrite -has_sup_Rdown -eqEF has_sup_Rdown. by rewrite -!supRE // -sup_Rdown eqEF sup_Rdown. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq order) mathcomp(ssralg ssrnum ssrint rat) Coq(Morphisms Setoid) fourcolor(real realsyntax realprop)