Commit 866daf89 by Guillaume Melquiond

### Add functions I.lower_complement and I.upper_complement.

parent 96f51ca0
 ... ... @@ -170,6 +170,18 @@ Definition upper_extent xi := | _ => Inan end. Definition lower_complement xi := match xi with | Ibnd xl _ => if F.real xl then Ibnd F.nan xl else empty | Inan => empty end. Definition upper_complement xi := match xi with | Ibnd _ xu => if F.real xu then Ibnd xu F.nan else empty | Inan => empty end. Definition whole := Ibnd F.nan F.nan. Definition lower xi := ... ... @@ -673,6 +685,46 @@ rewrite F.nan_correct. exact I. Qed. Theorem lower_complement_correct : forall xi x y, contains (convert xi) (Xreal x) -> contains (convert (lower_complement xi)) (Xreal y) -> (y <= x)%R. Proof. intros [|xl xu] x y. intros _ H. now apply empty_correct in H. intros [H _]. simpl. rewrite F.real_correct. case_eq (F.toX xl). intros _ H'. now apply empty_correct in H'. intros l Hl [_ H']. rewrite Hl in H, H'. now apply Rle_trans with l. Qed. Theorem upper_complement_correct : forall xi x y, contains (convert xi) (Xreal x) -> contains (convert (upper_complement xi)) (Xreal y) -> (x <= y)%R. Proof. intros [|xl xu] x y. intros _ H. now apply empty_correct in H. intros [_ H]. simpl. rewrite F.real_correct. case_eq (F.toX xu). intros _ H'. now apply empty_correct in H'. intros u Hu [H' _]. rewrite Hu in H, H'. now apply Rle_trans with u. Qed. Theorem whole_correct : forall x, contains (convert whole) (Xreal x). ... ...
 ... ... @@ -406,6 +406,21 @@ Parameter whole_correct : forall x, contains (convert whole) (Xreal x). Parameter lower_complement : type -> type. Parameter upper_complement : type -> type. Parameter lower_complement_correct : forall xi x y, contains (convert xi) (Xreal x) -> contains (convert (lower_complement xi)) (Xreal y) -> (y <= x)%R. Parameter upper_complement_correct : forall xi x y, contains (convert xi) (Xreal x) -> contains (convert (upper_complement xi)) (Xreal y) -> (x <= y)%R. Parameter lower : type -> bound_type. Parameter upper : type -> bound_type. ... ...
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