From a5a3d944e528c6006f0ea901dded7c79367adb75 Mon Sep 17 00:00:00 2001
From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Tue, 29 Sep 2009 14:03:50 +0000
Subject: [PATCH] ...

---
 helm/software/matita/nlibrary/sets/sets.ma | 39 +++++++++++++++++++---
 1 file changed, 34 insertions(+), 5 deletions(-)

diff --git a/helm/software/matita/nlibrary/sets/sets.ma b/helm/software/matita/nlibrary/sets/sets.ma
index c21751c21..b644c4f42 100644
--- a/helm/software/matita/nlibrary/sets/sets.ma
+++ b/helm/software/matita/nlibrary/sets/sets.ma
@@ -83,13 +83,21 @@ nrecord qpowerclass (A: setoid) : Type[1] ≝
                 ma la sintassi :> non lo supporta *)
    mem_ok': ∀x,x':A. x=x' → (x ∈ pc) = (x' ∈ pc) 
  }.
+ 
+notation > "𝛀 ^ term 90 A" non associative with precedence 70 
+for @{ 'qpowerclass $A }.
 
-ndefinition Full_set: ∀A. qpowerclass A.
+notation "Ω term 90 A \atop ≈" non associative with precedence 70 
+for @{ 'qpowerclass $A }.
+
+interpretation "qpowerclass" 'qpowerclass a = (qpowerclass 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 ?.
 
-ndefinition qseteq: ∀A. equivalence_relation1 (qpowerclass A).
+ndefinition qseteq: ∀A. equivalence_relation1 (𝛀^A).
  #A; @
   [ napply (λS,S'. S = S')
   | #S; napply (refl1 ? (seteq A))
@@ -104,7 +112,7 @@ ndefinition qpowerclass_setoid: setoid → setoid1.
 nqed.
               
 unification hint 0 ≔ A ⊢  
-  carr1 (mk_setoid1 (qpowerclass A) (eq1 (qpowerclass_setoid A))) 
+  carr1 (mk_setoid1 (𝛀^A) (eq1 (qpowerclass_setoid A))) 
 ≡ qpowerclass A.
 
 ncoercion pc' : ∀A.∀x:qpowerclass_setoid A. Ω^A ≝ pc 
@@ -144,7 +152,7 @@ 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. qpowerclass A → qpowerclass A → qpowerclass A.
+nlemma intersect_ok: ∀A. 𝛀^A → 𝛀^A → 𝛀^A.
  #A; #S; #S'; @ (S ∩ S');
  #a; #a'; #Ha; @; *; #H1; #H2; @
   [##1,2: napply (. Ha^-1‡#); nassumption;
@@ -183,11 +191,32 @@ ndefinition prop21_mem :
 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; 
+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.
+
+
     
     
 nlemma test: ∀U.∀A,B:qpowerclass U. A ∩ B = A →
  ∀x,y. x=y → x ∈ A → y ∈ A ∩ B.
- #U; #A; #B; #H; #x; #y; #K; #K2; napply (. K^-1‡(H^-1‡#)); nassumption;
+ #U; #A; #B; #H; #x; #y; #K; #K2;
+ alias symbol "prop2" = "prop21".
+alias symbol "invert" = "setoid1 symmetry".
+napply (. (K^-1 ‡ (prop21 ??? (intersect_ok'' U) ???? H^-1 #))); STOP
+ 
+ napply (. K^-1‡(H^-1‡#)); nassumption;
 nqed. 
 
 (*
-- 
2.39.2