proposition: Theorem eval_RInt_contains_correct : forall prec deg limit vars hyps pf pu pv cf cu cv b, no_floor_prog pf = true -> eval_RInt_contains prec deg limit hyps pf pu pv cf cu cv b = true -> eval_hyps hyps vars ( contains (I.convert b) (Xreal (RInt (fun t => Prog.eval_real' pf (t :: vars) cf) (Prog.eval_real' pu vars cu) (Prog.eval_real' pv vars cv)))).
proof: Proof. intros prec deg limit vars hyps pf pu pv cf cu cv b Hp H. apply (R.eval_hyps_bnd_correct prec). intros H'. apply I.subset_correct with (2 := H). now apply contains_RInt. Qed.
imports: Coq(Reals List ZArith Psatz) Flocq(Zaux) Coquelicot(Coquelicot) Stdlib Coquelicot Xreal Basic Sig Interval Integral Eval Bertrand Tree Prog Reify Refine Interval_helper