proposition: Theorem real_value_implies_rep: forall alpha r, real_value alpha = r -> rep alpha r.
proof: Proof. intros [[ | | ] alpha] r Hrep. rewrite real_value_L in Hrep; rewrite <- Hrep; apply (rep_L alpha (Cons LL alpha) (real_value alpha) (real_value_base_interval alpha) (rep_real_value alpha) (EqSt_reflex _)). rewrite real_value_R in Hrep; rewrite <- Hrep; apply (rep_R alpha (Cons RR alpha) (real_value alpha) (real_value_base_interval alpha) (rep_real_value alpha) (EqSt_reflex _)). rewrite real_value_M in Hrep; rewrite <- Hrep; apply (rep_M alpha (Cons MM alpha) (real_value alpha) (real_value_base_interval alpha) (rep_real_value alpha) (EqSt_reflex _)). Qed.
imports: digits ub rep Rseries Rdefinitions RIneq Rcomplete QArithSternBrocot(R_addenda) Fourier_solvable_ineqs