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(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2019       *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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(** Proof that classical reals are constructive reals with extra properties, namely total order, existence of all least upper bounds and setoid equivalence simplifying to Leibniz equality.  From this point of view, the quotient Rabst and Rrepr between classical Dedekind reals and constructive Cauchy reals becomes an isomorphism for the ConstructiveReals structure.  This allows to apply results from constructive reals to classical reals. *)
Local Open Scope R_scope.

Lemma RdisjunctEpsilon
: forall a b c d : R, (a < b)%R \/ (c < d)%R -> (a < b)%R + (c < d)%R.