X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdatatypes%2Fsubsets.ma;h=8e2eda4c99508749053bc3041154e814cdf27fd6;hb=dc74ed7c4af1aa9b90fc5d2f0a86bd7825696e71;hp=5483dfa37f1fd648a38eca5727cd9cb9d05cc134;hpb=da03907a38982b8b45459213f2b9581accac5143;p=helm.git

diff --git a/helm/software/matita/library/datatypes/subsets.ma b/helm/software/matita/library/datatypes/subsets.ma
index 5483dfa37..8e2eda4c9 100644
--- a/helm/software/matita/library/datatypes/subsets.ma
+++ b/helm/software/matita/library/datatypes/subsets.ma
@@ -26,6 +26,8 @@ theorem transitive_subseteq_operator: ∀A. transitive ? (subseteq_operator A).
  assumption.
 qed.
 
+(*
+
 definition powerset_setoid: setoid → setoid1.
  intros (T);
  constructor 1;
@@ -57,7 +59,7 @@ definition mem: ∀A. binary_morphism1 A (Ω \sup A) CPROP.
      | apply s1; assumption]]
 qed.     
 
-interpretation "mem" 'mem a S = (fun1 ___ (mem _) a S).
+interpretation "mem" 'mem a S = (fun1 ??? (mem ?) a S).
 
 definition subseteq: ∀A. binary_morphism1 (Ω \sup A) (Ω \sup A) CPROP.
  intros;
@@ -72,7 +74,15 @@ definition subseteq: ∀A. binary_morphism1 (Ω \sup A) (Ω \sup A) CPROP.
       apply (transitive_subseteq_operator ???? s s4) ]]
 qed.
 
-interpretation "subseteq" 'subseteq U V = (fun1 ___ (subseteq _) U V).
+interpretation "subseteq" 'subseteq U V = (fun1 ??? (subseteq ?) U V).
+
+theorem subseteq_refl: ∀A.∀S:Ω \sup A.S ⊆ S.
+ intros 4; assumption.
+qed.
+
+theorem subseteq_trans: ∀A.∀S1,S2,S3: Ω \sup A. S1 ⊆ S2 → S2 ⊆ S3 → S1 ⊆ S3.
+ intros; apply transitive_subseteq_operator; [apply S2] assumption.
+qed.
 
 definition overlaps: ∀A. binary_morphism1 (Ω \sup A) (Ω \sup A) CPROP.
  intros;
@@ -86,7 +96,7 @@ definition overlaps: ∀A. binary_morphism1 (Ω \sup A) (Ω \sup A) CPROP.
      | apply (. #‡(H1 \sup -1)); assumption]]
 qed.
 
-interpretation "overlaps" 'overlaps U V = (fun1 ___ (overlaps _) U V).
+interpretation "overlaps" 'overlaps U V = (fun1 ??? (overlaps ?) U V).
 
 definition intersects:
  ∀A. binary_morphism1 (powerset_setoid A) (powerset_setoid A) (powerset_setoid A).
@@ -100,7 +110,7 @@ definition intersects:
     | apply (. (#‡(H \sup -1))‡(#‡(H1 \sup -1))); assumption]]
 qed.
 
-interpretation "intersects" 'intersects U V = (fun1 ___ (intersects _) U V).
+interpretation "intersects" 'intersects U V = (fun1 ??? (intersects ?) U V).
 
 definition union:
  ∀A. binary_morphism1 (powerset_setoid A) (powerset_setoid A) (powerset_setoid A).
@@ -114,14 +124,19 @@ definition union:
     | apply (. (#‡(H \sup -1))‡(#‡(H1 \sup -1))); assumption]]
 qed.
 
-interpretation "union" 'union U V = (fun1 ___ (union _) U V).
+interpretation "union" 'union U V = (fun1 ??? (union ?) U V).
 
-definition singleton: ∀A:setoid. A → Ω \sup A.
- apply (λA:setoid.λa:A.{b | a=b});
- intros; simplify;
- split; intro;
- apply (.= H1);
-  [ apply H | apply (H \sup -1) ]
+definition singleton: ∀A:setoid. unary_morphism A (Ω \sup A).
+ intros; constructor 1;
+  [ apply (λA:setoid.λa:A.{b | a=b});
+    intros; simplify;
+    split; intro;
+    apply (.= H1);
+     [ apply H | apply (H \sup -1) ]
+  | intros; split; intros 2; simplify in f ⊢ %; apply trans;
+     [ apply a |4: apply a'] try assumption; apply sym; assumption]
 qed.
 
-interpretation "singleton" 'singl a = (singleton _ a).
+interpretation "singleton" 'singl a = (fun_1 ?? (singleton ?) a).
+
+*)
\ No newline at end of file