added auto_cache in the dupable status after an

[helm.git] / helm / software / matita / nlibrary / sets / sets.ma

diff --git a/helm/software/matita/nlibrary/sets/sets.ma b/helm/software/matita/nlibrary/sets/sets.ma
index f230957a765e1f877af40378ccd1e9269ac38dd6..623f676e96d944a4437dee92307063322e33c717 100644 (file)
--- a/helm/software/matita/nlibrary/sets/sets.ma
+++ b/helm/software/matita/nlibrary/sets/sets.ma
@@ -138,11 +138,10 @@ unification hint 0 ≔  A:setoid, x, S;
      TT ≟ (mk_binary_morphism1 ??? 
              (λx:setoid1_of_setoid ?.λS:ext_powerclass_setoid ?. x ∈ S) 
              (prop21 ??? (mem_ext_powerclass_setoid_is_morph A))),
-     M1 ≟ ?,
-     M2 ≟ ?,
-     M3 ≟ ?        
+     XX ≟ (ext_powerclass_setoid A)
   (*-------------------------------------*) ⊢ 
-      fun21 M1 M2 M3 TT x S ≡ mem A SS x.
+      fun21 (setoid1_of_setoid A) XX CPROP TT x S 
+    ≡ mem A SS x.
 
 nlemma subseteq_is_morph: ∀A. binary_morphism1 (ext_powerclass_setoid A) (ext_powerclass_setoid A) CPROP.
  #A; @
@@ -193,14 +192,8 @@ unification hint 0 ≔
     fun21 (powerclass_setoid A) (powerclass_setoid A) (powerclass_setoid A) R B C 
   ≡ intersect ? B C.
 
-ndefinition prop21_mem : 
-  ∀A,C.∀f:binary_morphism1 (setoid1_of_setoid A) (ext_powerclass_setoid A) C.
-   ∀a,a':setoid1_of_setoid A.
-    ∀b,b':ext_powerclass_setoid A.a = a' → b = b' → f a b = f a' b'.
-#A; #C; #f; #a; #a'; #b; #b'; #H1; #H2; napply prop21; nassumption;
-nqed.
-    
-interpretation "prop21 mem" 'prop2 l r = (prop21_mem ??????? l r).
+interpretation "prop21 mem" 'prop2 l r = (prop21 (setoid1_of_setoid ?) (ext_powerclass_setoid ?) ? ???? l r).
+interpretation "prop21 ext" 'prop2 l r = (prop21 (ext_powerclass_setoid ?) (ext_powerclass_setoid ?) ? ???? l r).
 
 nlemma intersect_is_ext_morph: 
  ∀A. binary_morphism1 (ext_powerclass_setoid A) (ext_powerclass_setoid A) (ext_powerclass_setoid A).
@@ -225,19 +218,30 @@ unification hint 1 ≔
             intersect (carr A) BB CC.
 
 (*
+alias symbol "hint_decl" = "hint_decl_Type2".
+unification hint 0 ≔
+  A : setoid, B,C : 𝛀^A ;
+  CC ≟ (ext_carr ? C),
+  BB ≟ (ext_carr ? B),
+  C1 ≟ (carr1 (powerclass_setoid (carr A))),
+  C2 ≟ (carr1 (ext_powerclass_setoid A))
+  ⊢ 
+     eq_rel1 C1 (eq1 (powerclass_setoid (carr A))) BB CC ≡ 
+          eq_rel1 C2 (eq1 (ext_powerclass_setoid A)) B C.
+          
+unification hint 0 ≔
+  A, B : CPROP ⊢ iff A B ≡ eq_rel1 ? (eq1 CPROP) A B.    
+*)
     
-    
-nlemma test: ∀U.∀A,B:qpowerclass U. A ∩ B = A →
+nlemma test: ∀U.∀A,B:𝛀^U. A ∩ B = A →
  ∀x,y. x=y → x ∈ A → y ∈ A ∩ B.
- #U; #A; #B; #H; #x; #y; #K; #K2; napply (. #‡(?));
-##[ nchange with (A ∩ B = ?);
-    napply (prop21 ??? (mk_binary_morphism1 … (λS,S'.S ∩ S') (prop21 … (intersect_ok' U))) A A B B ##);
-    #H; napply H;
+ #U; #A; #B; #H; #x; #y; #K; #K2;
+napply (. (prop21 ??? ? ???? K^-1 (H^-1‡#)));
   nassumption;
 nqed. 
 
-(*
-nlemma intersect_ok: ∀A. binary_morphism1 (qpowerclass_setoid A) (qpowerclass_setoid A) (qpowerclass_setoid A).
+
+nlemma intersect_ok: ∀A. binary_morphism1 (ext_powerclass_setoid A) (ext_powerclass_setoid A) (ext_powerclass_setoid A).
  #A; @
   [ #S; #S'; @
      [ napply (S ∩ S')
@@ -267,6 +271,7 @@ nlemma test: ∀A:setoid. ∀U,V:qpowerclass A. ∀x,x':setoid1_of_setoid A. x=x
  #A; #U; #V; #x; #x'; #H; #p; napply (. (H^-1‡#)); nassumption.
 nqed.
 *)
+*)
 
 ndefinition image: ∀A,B. (carr A → carr B) → Ω^A → Ω^B ≝
  λA,B:setoid.λf:carr A → carr B.λSa:Ω^A.
@@ -317,11 +322,11 @@ nlemma first_omomorphism_theorem_functions1:
 nqed.
 
 ndefinition surjective ≝
- λA,B.λS: qpowerclass A.λT: qpowerclass B.λf:unary_morphism A B.
+ λA,B.λS: ext_powerclass A.λT: ext_powerclass B.λf:unary_morphism A B.
   ∀y. y ∈ T → ∃x. x ∈ S ∧ f x = y.
 
 ndefinition injective ≝
- λA,B.λS: qpowerclass A.λf:unary_morphism A B.
+ λA,B.λS: ext_powerclass A.λf:unary_morphism A B.
   ∀x,x'. x ∈ S → x' ∈ S → f x = f x' → x = x'.
 
 nlemma first_omomorphism_theorem_functions2:
@@ -337,7 +342,7 @@ nlemma first_omomorphism_theorem_functions3:
  #A; #B; #f; nwhd; #x; #x'; #Hx; #Hx'; #K; nassumption.
 nqed.
 
-nrecord isomorphism (A, B : setoid) (S: qpowerclass A) (T: qpowerclass B) : Type[0] ≝
+nrecord isomorphism (A, B : setoid) (S: ext_powerclass A) (T: ext_powerclass B) : Type[0] ≝
  { iso_f:> unary_morphism A B;
    f_closed: ∀x. x ∈ S → iso_f x ∈ T;
    f_sur: surjective … S T iso_f;
@@ -365,4 +370,3 @@ ncheck (λA:?.
    ;
  }.
 *)
-*)
\ No newline at end of file