snapshot for CSC

[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 4579054c5bd13096635804a796196d57a4a092e5..2f0725d851284586220445d860c03a72d15163e6 100644 (file)
--- a/helm/software/matita/nlibrary/sets/sets.ma
+++ b/helm/software/matita/nlibrary/sets/sets.ma
@@ -1,3 +1,4 @@
+
 (**************************************************************************)
 (*       ___                                                              *)
 (*      ||M||                                                             *)
@@ -39,8 +40,7 @@ ndefinition big_union ≝ λA,B.λT:Ω \sup A.λf:A → Ω \sup B.{ x | ∃i. i
 ndefinition big_intersection ≝ λA,B.λT:Ω \sup A.λf:A → Ω \sup B.{ x | ∀i. i ∈ T → x ∈ f i }.
 
 ndefinition full_set: ∀A. Ω \sup A ≝ λA.{ x | True }.
-(* bug dichiarazione coercion qui *)
-(* ncoercion full_set : ∀A:Type[0]. Ω \sup A ≝ full_set on _A: Type[0] to (Ω \sup ?). *)
+ncoercion full_set : ∀A:Type[0]. Ω \sup A ≝ full_set on A: Type[0] to (Ω \sup ?).
 
 nlemma subseteq_refl: ∀A.∀S: Ω \sup A. S ⊆ S.
  #A; #S; #x; #H; nassumption.
@@ -69,27 +69,29 @@ ndefinition powerclass_setoid: Type[0] → setoid1.
   | napply seteq ]
 nqed.
 
-unification hint 0 (∀A. (λx,y.True) (carr1 (powerclass_setoid A)) (Ω \sup A)).
+include "hints_declaration.ma". 
+
+alias symbol "hint_decl" = "hint_decl_Type2".
+unification hint 0 ≔ A : ? ⊢ carr1 (powerclass_setoid A) ≡ Ω^A.
 
 (************ SETS OVER SETOIDS ********************)
 
 include "logic/cprop.ma".
 
 nrecord qpowerclass (A: setoid) : Type[1] ≝
- { pc:> Ω \sup A;
+ { pc:> Ω^A;
    mem_ok': ∀x,x':A. x=x' → (x ∈ pc) = (x' ∈ pc) 
  }.
 
 ndefinition Full_set: ∀A. qpowerclass A.
  #A; napply mk_qpowerclass
   [ napply (full_set A)
-  | #x; #x'; #H; nnormalize in ⊢ (?%?%%); (* bug universi qui napply refl1;*)
-    napply mk_iff; #K; nassumption ]
+  | #x; #x'; #H; napply refl1; ##]
 nqed.
 
 ndefinition qseteq: ∀A. equivalence_relation1 (qpowerclass A).
  #A; napply mk_equivalence_relation1
-  [ napply (λS,S':qpowerclass A. eq_rel1 ? (eq1 (powerclass_setoid A)) S S')
+  [ napply (λS,S':qpowerclass A. S = S')
   | #S; napply (refl1 ? (seteq A))
   | #S; #S'; napply (sym1 ? (seteq A))
   | #S; #T; #U; napply (trans1 ? (seteq A))]
@@ -101,31 +103,29 @@ ndefinition qpowerclass_setoid: setoid → setoid1.
   | napply (qseteq A) ]
 nqed.
 
-unification hint 0 (∀A. (λx,y.True) (carr1 (qpowerclass_setoid A)) (qpowerclass A)).
-ncoercion qpowerclass_hint: ∀A: setoid. ∀S: qpowerclass_setoid A. Ω \sup A ≝ λA.λS.S
- on _S: (carr1 (qpowerclass_setoid ?)) to (Ω \sup ?). 
+unification hint 0 ≔ A : ? ⊢  carr1 (qpowerclass_setoid A) ≡ qpowerclass A.
 
 nlemma mem_ok: ∀A. binary_morphism1 (setoid1_of_setoid A) (qpowerclass_setoid A) CPROP.
  #A; napply mk_binary_morphism1
-  [ napply (λx.λS: qpowerclass_setoid A. x ∈ S) (* CSC: ??? *)
-  | #a; #a'; #b; #b'; #Ha; #Hb; (* CSC: qui *; non funziona *)
-    nwhd; nwhd in ⊢ (? (? % ??) (? % ??)); napply mk_iff; #H
-     [ ncases Hb; #Hb1; #_; napply Hb1; napply (. (mem_ok' …))
-        [ nassumption | napply Ha^-1 | ##skip ]
-   ##| ncases Hb; #_; #Hb2; napply Hb2; napply (. (mem_ok' …))
-        [ nassumption | napply Ha | ##skip ]##]
+  [ #x; napply (λS: qpowerclass_setoid ?. x ∈ S) (* ERROR CSC: ??? *)
+  | #a; #a'; #b; #b'; #Ha; *; #Hb1; #Hb2; napply mk_iff; #H;
+     ##[ napply Hb1; napply (. (mem_ok' …)); ##[##3: napply H| napply Ha^-1;##]
+     ##| napply Hb2; napply (. (mem_ok' …)); ##[##3: napply H| napply Ha;##]
+     ##]
+  ##]
 nqed.
 
-unification hint 0 (∀A,x,S. (λx,y.True) (fun21 ??? (mem_ok A) x S) (mem A S x)).
+unification hint 0 ≔ 
+  A : setoid, x : ?, S : ? ⊢ (mem_ok A) x S ≡ mem A S x.
   
 nlemma subseteq_ok: ∀A. binary_morphism1 (qpowerclass_setoid A) (qpowerclass_setoid A) CPROP.
  #A; napply mk_binary_morphism1
   [ napply (λS,S': qpowerclass_setoid ?. S ⊆ S')
   | #a; #a'; #b; #b'; *; #Ha1; #Ha2; *; #Hb1; #Hb2; napply mk_iff; #H
-     [ napply (subseteq_trans … a' a) (* anche qui, perche' serve a'? *)
-        [ nassumption | napply (subseteq_trans … a b); nassumption ]
-   ##| napply (subseteq_trans … a a') (* anche qui, perche' serve a'? *)
-        [ nassumption | napply (subseteq_trans … a' b'); nassumption ] ##]
+     [ napply (subseteq_trans … a)
+        [ nassumption | napply (subseteq_trans … b); nassumption ]
+   ##| napply (subseteq_trans … a')
+        [ nassumption | napply (subseteq_trans … b'); nassumption ] ##]
 nqed.
 
 nlemma intersect_ok: ∀A. binary_morphism1 (qpowerclass_setoid A) (qpowerclass_setoid A) (qpowerclass_setoid A).
@@ -133,14 +133,17 @@ nlemma intersect_ok: ∀A. binary_morphism1 (qpowerclass_setoid A) (qpowerclass_
   [ #S; #S'; napply mk_qpowerclass
      [ napply (S ∩ S')
      | #a; #a'; #Ha; nwhd in ⊢ (? ? ? % %); napply mk_iff; *; #H1; #H2; napply conj
-        [##1,2: napply (. (mem_ok' …)^-1) [##3,6: nassumption |##1,4: nassumption |##*: ##skip]
-      ##|##3,4: napply (. (mem_ok' …)) [##2,5: nassumption |##1,4: nassumption |##*: ##skip]##]##]
+        [##1,2: napply (. (mem_ok' …)^-1) [##3,6: nassumption |##2,5: nassumption |##*: ##skip]
+      ##|##3,4: napply (. (mem_ok' …)) [##1,3,4,6: nassumption |##*: ##skip]##]##]
  ##| #a; #a'; #b; #b'; #Ha; #Hb; nwhd; napply conj; #x; nwhd in ⊢ (% → %); #H
       [ napply (. ((#‡Ha^-1)‡(#‡Hb^-1))); nassumption
       | napply (. ((#‡Ha)‡(#‡Hb))); nassumption ]##]
 nqed.
 
-unification hint 0 (∀A.∀U,V.(λx,y.True) (fun21 ??? (intersect_ok A) U V) (intersect A U V)).
+(*
+unification hint 0 ≔ 
+   A : setoid, U : qpowerclass_setoid A, V : ? ⊢ (intersect_ok A) U V ≡ U ∩ V.
+  *)
 
 nlemma test: ∀A:setoid. ∀U,V:qpowerclass A. ∀x,x':setoid1_of_setoid A. x=x' → x ∈ U ∩ V → x' ∈ U ∩ V.
  #A; #U; #V; #x; #x'; #H; #p;