hints fixed

diff --git a/helm/software/matita/nlibrary/sets/sets.ma b/helm/software/matita/nlibrary/sets/sets.ma
index b09c206ab774370c2a232f347c84425aecb717b4..f230957a765e1f877af40378ccd1e9269ac38dd6 100644 (file)
--- a/helm/software/matita/nlibrary/sets/sets.ma
+++ b/helm/software/matita/nlibrary/sets/sets.ma
@@ -77,27 +77,27 @@ unification hint 0 ≔ A ⊢ carr1 (mk_setoid1 (Ω^A) (eq1 (powerclass_setoid A)
 
 include "logic/cprop.ma".
 
-nrecord qpowerclass (A: setoid) : Type[1] ≝
- { pc:> Ω^A; (* qui pc viene dichiarato con un target preciso... 
+nrecord ext_powerclass (A: setoid) : Type[1] ≝
+ { ext_carr:> Ω^A; (* qui pc viene dichiarato con un target preciso... 
                 forse lo si vorrebbe dichiarato con un target più lasco 
                 ma la sintassi :> non lo supporta *)
-   mem_ok': ∀x,x':A. x=x' → (x ∈ pc) = (x' ∈ pc) 
+   ext_prop: ∀x,x':A. x=x' → (x ∈ ext_carr) = (x' ∈ ext_carr) 
  }.
  
 notation > "𝛀 ^ term 90 A" non associative with precedence 70 
-for @{ 'qpowerclass $A }.
+for @{ 'ext_powerclass $A }.
 
 notation "Ω term 90 A \atop ≈" non associative with precedence 70 
-for @{ 'qpowerclass $A }.
+for @{ 'ext_powerclass $A }.
 
-interpretation "qpowerclass" 'qpowerclass a = (qpowerclass a).
+interpretation "extensional powerclass" 'ext_powerclass a = (ext_powerclass a).
 
 ndefinition Full_set: ∀A. 𝛀^A.
  #A; @[ napply A | #x; #x'; #H; napply refl1]
 nqed.
-ncoercion Full_set: ∀A. qpowerclass A ≝ Full_set on A: setoid to qpowerclass ?.
+ncoercion Full_set: ∀A. ext_powerclass A ≝ Full_set on A: setoid to ext_powerclass ?.
 
-ndefinition qseteq: ∀A. equivalence_relation1 (𝛀^A).
+ndefinition ext_seteq: ∀A. equivalence_relation1 (𝛀^A).
  #A; @
   [ napply (λS,S'. S = S')
   | #S; napply (refl1 ? (seteq A))
@@ -105,40 +105,46 @@ ndefinition qseteq: ∀A. equivalence_relation1 (𝛀^A).
   | #S; #T; #U; napply (trans1 ? (seteq A))]
 nqed.
 
-ndefinition qpowerclass_setoid: setoid → setoid1.
+ndefinition ext_powerclass_setoid: setoid → setoid1.
  #A; @
-  [ napply (qpowerclass A)
-  | napply (qseteq A) ]
+  [ napply (ext_powerclass A)
+  | napply (ext_seteq A) ]
 nqed.
               
-unification hint 0 ≔ A ⊢  
-  carr1 (mk_setoid1 (𝛀^A) (eq1 (qpowerclass_setoid A))) 
-≡ qpowerclass A.
+unification hint 0 ≔ A;
+      R ≟ (mk_setoid1 (𝛀^A) (eq1 (ext_powerclass_setoid A)))
+  (* ----------------------------------------------------- *) ⊢  
+                 carr1 R ≡ ext_powerclass A.
 
-ncoercion pc' : ∀A.∀x:qpowerclass_setoid A. Ω^A ≝ pc 
-on _x : (carr1 (qpowerclass_setoid ?)) to (Ω^?). 
+                
+(*
+ncoercion ext_carr' : ∀A.∀x:ext_powerclass_setoid A. Ω^A ≝ ext_carr 
+on _x : (carr1 (ext_powerclass_setoid ?)) to (Ω^?). 
+*)
 
-nlemma mem_ok: ∀A. binary_morphism1 (setoid1_of_setoid A) (qpowerclass_setoid A) CPROP.
+nlemma mem_ext_powerclass_setoid_is_morph: 
+ ∀A. binary_morphism1 (setoid1_of_setoid A) (ext_powerclass_setoid A) CPROP.
  #A; @
   [ napply (λx,S. x ∈ S) 
   | #a; #a'; #b; #b'; #Ha; *; #Hb1; #Hb2; @; #H;
-     ##[ napply Hb1; napply (. (mem_ok' …)); ##[##3: napply H| napply Ha^-1;##]
-     ##| napply Hb2; napply (. (mem_ok' …)); ##[##3: napply H| napply Ha;##]
+     ##[ napply Hb1; napply (. (ext_prop … Ha^-1)); nassumption;
+     ##| napply Hb2; napply (. (ext_prop … Ha)); nassumption;
      ##]
   ##]
 nqed.
 
 unification hint 0 ≔  A:setoid, x, S;  
-         SS ≟ (pc ? S),
-         TT ≟ (mk_binary_morphism1 ??? 
-                 (λx:setoid1_of_setoid ?.λS:qpowerclass_setoid ?. x ∈ S) 
-                 (prop21 ??? (mem_ok A)))
-           
+     SS ≟ (ext_carr ? 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 ≟ ?        
   (*-------------------------------------*) ⊢ 
-    fun21 ? ? ? TT x S 
-  ≡ mem A SS x.
+      fun21 M1 M2 M3 TT x S ≡ mem A SS x.
 
-nlemma subseteq_ok: ∀A. binary_morphism1 (qpowerclass_setoid A) (qpowerclass_setoid A) CPROP.
+nlemma subseteq_is_morph: ∀A. binary_morphism1 (ext_powerclass_setoid A) (ext_powerclass_setoid A) CPROP.
  #A; @
   [ napply (λS,S'. S ⊆ S')
   | #a; #a'; #b; #b'; *; #Ha1; #Ha2; *; #Hb1; #Hb2; @; #H
@@ -152,7 +158,7 @@ unification hint 0 ≔ A,a,a'
  (*-----------------------------------------------------------------*) ⊢
   eq_rel ? (eq A) a a' ≡ eq_rel1 ? (eq1 (setoid1_of_setoid A)) a a'.
 
-nlemma intersect_ok: ∀A. 𝛀^A → 𝛀^A → 𝛀^A.
+nlemma intersect_is_ext: ∀A. 𝛀^A → 𝛀^A → 𝛀^A.
  #A; #S; #S'; @ (S ∩ S');
  #a; #a'; #Ha; @; *; #H1; #H2; @
   [##1,2: napply (. Ha^-1‡#); nassumption;
@@ -160,19 +166,15 @@ nlemma intersect_ok: ∀A. 𝛀^A → 𝛀^A → 𝛀^A.
 nqed.
 
 alias symbol "hint_decl" = "hint_decl_Type1".
-unification hint 1 ≔ 
-  A : setoid, B,C : qpowerclass A ⊢ 
-    pc A (mk_qpowerclass ? (B ∩ C) (mem_ok' ? (intersect_ok ? B C))) 
-    ≡ intersect ? (pc ? B) (pc ? C).
-
-unification hint 1 ≔ 
-  A : setoid, B,C : qpowerclass A;
-  DX ≟ (intersect ? (pc ? B) (pc ? C)),
-  SX ≟ (mk_qpowerclass ? (B ∩ C) (mem_ok' ? (intersect_ok ? B C)))
- (*-----------------------------------------------------------------*) ⊢
-  pc A SX  ≡ DX.
-
-nlemma intersect_ok': ∀A. binary_morphism1 (powerclass_setoid A) (powerclass_setoid A) (powerclass_setoid A).
+unification hint 0 ≔ 
+  A : setoid, B,C : ext_powerclass A;
+  R ≟ (mk_ext_powerclass ? (B ∩ C) (ext_prop ? (intersect_is_ext ? B C)))
+  
+  (* ------------------------------------------*)  ⊢ 
+    ext_carr A R ≡ intersect ? (ext_carr ? B) (ext_carr ? C).
+
+nlemma intersect_is_morph: 
+ ∀A. binary_morphism1 (powerclass_setoid A) (powerclass_setoid A) (powerclass_setoid A).
  #A; @ (λS,S'. S ∩ S');
  #a; #a'; #b; #b'; *; #Ha1; #Ha2; *; #Hb1; #Hb2; @; #x; nnormalize; *; #Ka; #Kb; @
   [ napply Ha1; nassumption
@@ -183,37 +185,46 @@ nqed.
 
 alias symbol "hint_decl" = "hint_decl_Type1".
 unification hint 0 ≔ 
-  A : Type[0], B,C : powerclass A ⊢ 
-    fun21 …
-     (mk_binary_morphism1 …
+  A : Type[0], B,C : Ω^A;
+  R ≟ (mk_binary_morphism1 …
        (λS,S'.S ∩ S') 
-       (prop21 … (intersect_ok' A))) B C
-    ≡ intersect ? B C.
+       (prop21 … (intersect_is_morph A)))
+   ⊢ 
+    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) (qpowerclass_setoid A) C.
+  ∀A,C.∀f:binary_morphism1 (setoid1_of_setoid A) (ext_powerclass_setoid A) C.
    ∀a,a':setoid1_of_setoid A.
-    ∀b,b':qpowerclass_setoid A.a = a' → b = b' → f a b = f a' b'.
+    ∀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).
 
-nlemma intersect_ok'': 
-  ∀A. binary_morphism1 (qpowerclass_setoid A) (qpowerclass_setoid A) (qpowerclass_setoid A).
- #A; @ (intersect_ok A); nlapply (prop21 … (intersect_ok' A)); #H;
- #a; #a'; #b; #b'; #H1; #H2; napply H; nassumption; 
+nlemma intersect_is_ext_morph: 
+ ∀A. binary_morphism1 (ext_powerclass_setoid A) (ext_powerclass_setoid A) (ext_powerclass_setoid A).
+ #A; @ (intersect_is_ext …); nlapply (prop21 … (intersect_is_morph A));
+#H; #a; #a'; #b; #b'; #H1; #H2; napply H; nassumption; 
 nqed.
 
 unification hint 1 ≔ 
-  A:?, B,C : 𝛀^A ⊢ 
-    fun21 …
-     (mk_binary_morphism1 …
-       (λS,S':qpowerclass_setoid A.S ∩ S') 
-       (prop21 … (intersect_ok'' A))) B C
-    ≡ intersect ? B C.
-
+      A:setoid, B,C : 𝛀^A;
+      R ≟ (mk_binary_morphism1 (ext_powerclass_setoid A) (ext_powerclass_setoid A) (ext_powerclass_setoid A)
+              (λS,S':carr1 (ext_powerclass_setoid A).
+                mk_ext_powerclass A (S∩S') (ext_prop A (intersect_is_ext ? S S'))) 
+              (prop21 … (intersect_is_ext_morph A))) ,
+       BB ≟ (ext_carr ? B),
+       CC ≟ (ext_carr ? C)
+   (* ------------------------------------------------------*) ⊢ 
+            ext_carr A
+             (fun21 
+              (ext_powerclass_setoid A) 
+              (ext_powerclass_setoid A) 
+              (ext_powerclass_setoid A) R B C) ≡ 
+            intersect (carr A) BB CC.
 
+(*
     
     
 nlemma test: ∀U.∀A,B:qpowerclass U. A ∩ B = A →
@@ -354,3 +365,4 @@ ncheck (λA:?.
    ;
  }.
 *)
+*)
\ No newline at end of file