- renamed ocaml/ to components/

[helm.git] / helm / matita / library / datatypes / bool.ma

diff --git a/helm/matita/library/datatypes/bool.ma b/helm/matita/library/datatypes/bool.ma
deleted file mode 100644 (file)
index 3292e67..0000000
--- a/helm/matita/library/datatypes/bool.ma
+++ /dev/null
@@ -1,126 +0,0 @@
-(**************************************************************************)
-(*       ___                                                               *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
-(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU Lesser General Public License Version 2.1         *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/datatypes/bool/".
-
-include "logic/equality.ma".
-
-inductive bool : Set \def 
-  | true : bool
-  | false : bool.
-
-theorem bool_elim: \forall P:bool \to Prop. \forall b:bool.
-  (b = true \to P true)
-  \to (b = false \to P false)
-  \to P b.
-  intros 2 (P b).
-  elim b;
-  [ apply H; reflexivity
-  | apply H1; reflexivity
-  ]
-qed.
-
-theorem not_eq_true_false : true \neq false.
-unfold Not.intro.
-change with 
-match true with
-[ true \Rightarrow False
-| flase \Rightarrow True].
-rewrite > H.simplify.exact I.
-qed.
-
-definition notb : bool \to bool \def
-\lambda b:bool. 
- match b with 
- [ true \Rightarrow false
- | false \Rightarrow true ].
- 
-theorem notb_elim: \forall b:bool.\forall P:bool \to Prop.
-match b with
-[ true \Rightarrow P false
-| false \Rightarrow P true] \to P (notb b).
-intros 2.elim b.exact H. exact H.
-qed.
-
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "boolean not" 'not x = (cic:/matita/datatypes/bool/notb.con x).
-
-definition andb : bool \to bool \to bool\def
-\lambda b1,b2:bool. 
- match b1 with 
- [ true \Rightarrow b2
- | false \Rightarrow false ].
-
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "boolean and" 'and x y = (cic:/matita/datatypes/bool/andb.con x y).
-
-theorem andb_elim: \forall b1,b2:bool. \forall P:bool \to Prop.
-match b1 with
-[ true \Rightarrow P b2
-| false \Rightarrow P false] \to P (b1 \land b2).
-intros 3.elim b1.exact H. exact H.
-qed.
-
-theorem andb_true_true: \forall b1,b2. (b1 \land b2) = true \to b1 = true.
-intro. elim b1.
-reflexivity.
-assumption.
-qed.
-
-definition orb : bool \to bool \to bool\def
-\lambda b1,b2:bool. 
- match b1 with 
- [ true \Rightarrow true
- | false \Rightarrow b2].
-
-theorem orb_elim: \forall b1,b2:bool. \forall P:bool \to Prop.
-match b1 with
-[ true \Rightarrow P true
-| false \Rightarrow P b2] \to P (orb b1 b2).
-intros 3.elim b1.exact H. exact H.
-qed.
-
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "boolean or" 'or x y = (cic:/matita/datatypes/bool/orb.con x y).
-
-definition if_then_else : bool \to Prop \to Prop \to Prop \def 
-\lambda b:bool.\lambda P,Q:Prop.
-match b with
-[ true \Rightarrow P
-| false  \Rightarrow Q].
-
-(*CSC: missing notation for if_then_else *)
-
-theorem bool_to_decidable_eq:
- \forall b1,b2:bool. decidable (b1=b2).
- intros.
- unfold decidable.
- elim b1.
-  elim b2.
-   left. reflexivity.
-   right. exact not_eq_true_false.
-  elim b2.
-   right. unfold Not. intro.
-   apply not_eq_true_false.
-   symmetry. exact H.
-   left. reflexivity.
-qed.
-
-theorem P_x_to_P_x_to_eq:
- \forall A:Set. \forall P: A \to bool.
-  \forall x:A. \forall p1,p2:P x = true. p1 = p2.
- intros.
- apply eq_to_eq_to_eq_p_q.
- exact bool_to_decidable_eq.
-qed.