proposition: Lemma rounded_le' `{Rounded A} : forall e u v, close e u v -> forall d, ' e <= ' d -> close d u v.
proof: Proof. intros e u v xi d E. apply le_equiv_lt in E. destruct E as [E|E]. - apply pos_eq in E. rewrite <-E;trivial. - pose proof (pos_eq _ (_ + _) (Qpos_diff_pr _ _ E)) as E'. rewrite E'. apply rounded_plus. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.rationals HoTT.Classes.interfaces.orders HoTT.Classes.implementations.peano_naturals HoTT.Classes.implementations.natpair_integers HoTT.Classes.theory.groups HoTT.Classes.theory.integers HoTT.Classes.theory.dec_fields HoTT.Classes.orders.dec_fields HoTT.Classes.orders.sum HoTT.Classes.theory.rationals HoTT.Classes.orders.lattices HoTT.Classes.implementations.assume_rationals HoTT.Classes.tactics.ring_quote HoTT.Classes.tactics.ring_tac