X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Fsets%2Fsetoids1.ma;h=69e0958744de4f83c3257f88ad3b8e4ac78ef8fa;hb=c57405141d26ac2215a07b05d27a16a691dda50e;hp=115d1f6438a94da500eb447aa3d715b3e74353d8;hpb=a580ff5c627c4148cdd3649ead20f4fac0f78be8;p=helm.git

diff --git a/helm/software/matita/nlibrary/sets/setoids1.ma b/helm/software/matita/nlibrary/sets/setoids1.ma
index 115d1f643..69e095874 100644
--- a/helm/software/matita/nlibrary/sets/setoids1.ma
+++ b/helm/software/matita/nlibrary/sets/setoids1.ma
@@ -56,21 +56,15 @@ nrecord unary_morphism1 (A,B: setoid1) : Type[1] ≝
    prop11: ∀a,a'. eq1 ? a a' → eq1 ? (fun11 a) (fun11 a')
  }.
 
-nrecord binary_morphism1 (A,B,C:setoid1) : Type[1] ≝
- { fun21:2> A → B → C;
-   prop21: ∀a,a',b,b'. eq1 ? a a' → eq1 ? b b' → eq1 ? (fun21 a b) (fun21 a' b')
- }.
-
 interpretation "prop11" 'prop1 c = (prop11 ????? c).
-interpretation "prop21" 'prop2 l r = (prop21 ???????? l r).
 interpretation "refl1" 'refl = (refl1 ???).
 
 ndefinition unary_morphism1_setoid1: setoid1 → setoid1 → setoid1.
  #s; #s1; @ (unary_morphism1 s s1); @
-     [ #f; #g; napply (∀a:s. f a = g a)
-     | #x; #a; napply refl1
-     | #x; #y; #H; #a; napply sym1; nauto
-     | #x; #y; #z; #H1; #H2; #a; napply trans1; ##[##2: napply H1 | ##skip | napply H2]##]
+     [ #f; #g; napply (∀a,a':s. a=a' → f a = g a')
+     | #x; #a; #a'; #Ha; napply (.= †Ha); napply refl1
+     | #x; #y; #H; #a; #a'; #Ha; napply (.= †Ha); napply sym1; /2/
+     | #x; #y; #z; #H1; #H2; #a; #a'; #Ha; napply (.= †Ha); napply trans1; ##[##2: napply H1 | ##skip | napply H2]//;##]
 nqed.
 
 unification hint 0 ≔ S, T ;
@@ -78,6 +72,18 @@ unification hint 0 ≔ S, T ;
 (* --------------------------------- *) ⊢
    carr1 R ≡ unary_morphism1 S T.
 
+interpretation "prop21" 'prop2 l r = (prop11 ? (unary_morphism1_setoid1 ??) ? ?? l ?? r).
+
+nlemma unary_morph1_eq1: ∀A,B.∀f,g: unary_morphism1 A B. (∀x. f x = g x) → f=g.
+/3/. nqed.
+
+nlemma mk_binary_morphism1:
+ ∀A,B,C: setoid1. ∀f: A → B → C. (∀a,a',b,b'. a=a' → b=b' → f a b = f a' b') →
+  unary_morphism1 A (unary_morphism1_setoid1 B C).
+ #A; #B; #C; #f; #H; @ [ #x; @ (f x) ] #a; #a'; #Ha [##2: napply unary_morph1_eq1; #y]
+ /2/.
+nqed.
+
 ndefinition composition1 ≝
  λo1,o2,o3:Type[1].λf:o2 → o3.λg: o1 → o2.λx.f (g x).
  
@@ -98,12 +104,11 @@ unification hint 0 ≔ o1,o2,o3:setoid1,f:unary_morphism1 o2 o3,g:unary_morphism
  (* -------------------------------------------------------------------- *) ⊢
                               fun11 ?? R ≡ (composition1 … f g).
                               
-ndefinition comp_binary_morphisms:
+ndefinition comp1_binary_morphisms:
  ∀o1,o2,o3.
-  binary_morphism1 (unary_morphism1_setoid1 o2 o3) (unary_morphism1_setoid1 o1 o2)
-   (unary_morphism1_setoid1 o1 o3).
-#o1; #o2; #o3; @
+  unary_morphism1 (unary_morphism1_setoid1 o2 o3)
+   (unary_morphism1_setoid1 (unary_morphism1_setoid1 o1 o2) (unary_morphism1_setoid1 o1 o3)).
+#o1; #o2; #o3; napply mk_binary_morphism1
  [ #f; #g; napply (comp1_unary_morphisms … f g) (*CSC: why not ∘?*)
- | #a; #a'; #b; #b'; #ea; #eb; #x; nnormalize;
-   napply (.= †(eb x)); napply ea.
-nqed.
+ | #a; #a'; #b; #b'; #ea; #eb; #x; #x'; #Hx; nnormalize; /3/ ]
+nqed.
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