proposition: Lemma inser_trans_R_depr : forall r1 r2 r3 r4, r1 <= r2 < r3 -> {r1 <= r2 < r4} + {r4 <= r2 < r3}.
proof: Proof. intros r1 r2 r3 r4 [H1 H2]; destruct (Rlt_le_dec r2 r4) as [Hlt | Hle]. - now left. - now right. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField