Quellcode-Bibliothek

^© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: OmegaPre.v Sprache: Coq

Original von: Coq^©

Require Import ZArith Nnat Omega.
Open Scope Z_scope.

(** Test of the zify preprocessor for (R)Omega *)

(* More details in file PreOmega.v

   (r)omega with Z        : starts with zify_op
   (r)omega with nat      : starts with zify_nat
   (r)omega with positive : starts with zify_positive
   (r)omega with N        : starts with uses zify_N
   (r)omega with *        : starts zify (a saturation of the others)
*)

(* zify_op *)

Goal forall a:Z, Z.max a a = a.
intros.
omega with *.
Qed.

Goal forall a b:Z, Z.max a b = Z.max b a.
intros.
omega with *.
Qed.

Goal forall a b c:Z, Z.max a (Z.max b c) = Z.max (Z.max a b) c.
intros.
omega with *.
Qed.

Goal forall a b:Z, Z.max a b + Z.min a b = a + b.
intros.
omega with *.
Qed.

Goal forall a:Z, (Z.abs a)*(Z.sgn a) = a.
intros.
zify.
intuition; subst; omega. (* pure multiplication: omega alone can't do it *)
Qed.

Goal forall a:Z, Z.abs a = a -> a >= 0.
intros.
omega with *.
Qed.

Goal forall a:Z, Z.sgn a = a -> a = 1 \/ a = 0 \/ a = -1.
intros.
omega with *.
Qed.

(* zify_nat *)

Goal forall m: nat, (m<2)%nat -> (0<= m+m <=2)%nat.
intros.
omega with *.
Qed.

Goal forall m:nat, (m<1)%nat -> (m=0)%nat.
intros.
omega with *.
Qed.

Goal forall m: nat, (m<=100)%nat -> (0<= m+m <=200)%nat.
intros.
omega with *.
Qed.
(* 2000 instead of 200: works, but quite slow *)

Goal forall m: nat, (m*m>=0)%nat.
intros.
omega with *.
Qed.

(* zify_positive *)

Goal forall m: positive, (m<2)%positive -> (2 <= m+m /\ m+m <= 2)%positive.
intros.
omega with *.
Qed.

Goal forall m:positive, (m<2)%positive -> (m=1)%positive.
intros.
omega with *.
Qed.

Goal forall m: positive, (m<=1000)%positive -> (2<=m+m/\m+m <=2000)%positive.
intros.
omega with *.
Qed.

Goal forall m: positive, (m*m>=1)%positive.
intros.
omega with *.
Qed.

(* zify_N *)

Goal forall m:N, (m<2)%N -> (0 <= m+m /\ m+m <= 2)%N.
intros.
omega with *.
Qed.

Goal forall m:N, (m<1)%N -> (m=0)%N.
intros.
omega with *.
Qed.

Goal forall m:N, (m<=1000)%N -> (0<=m+m/\m+m <=2000)%N.
intros.
omega with *.
Qed.

Goal forall m:N, (m*m>=0)%N.
intros.
omega with *.
Qed.

(* mix of datatypes *)

Goal forall p, Z.of_N (N.of_nat (N.to_nat (Npos p))) = Zpos p.
intros.
omega with *.
Qed.

¤ Dauer der Verarbeitung: 0.16 Sekunden (vorverarbeitet) ¤

Download des Quellennavigators
Download des sprechenden Kalenders
in der Quellcodebibliothek suchen

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.