Work in Progress: Who needs binary_morphisms? Curryfication is your friend.

[helm.git] / helm / software / matita / nlibrary / sets / setoids1.ma

diff --git a/helm/software/matita/nlibrary/sets/setoids1.ma b/helm/software/matita/nlibrary/sets/setoids1.ma
index 49d259d5dd46ddb0d7efff2f0bf532794d8589df..fa615c8e4d74600903d6e1cdd845eb3524ad6f3f 100644 (file)
--- 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; //
-     | #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).
  
@@ -98,6 +104,7 @@ unification hint 0 ≔ o1,o2,o3:setoid1,f:unary_morphism1 o2 o3,g:unary_morphism
  (* -------------------------------------------------------------------- *) ⊢
                               fun11 ?? R ≡ (composition1 … f g).
                               
+(*
 ndefinition comp_binary_morphisms:
  ∀o1,o2,o3.
   binary_morphism1 (unary_morphism1_setoid1 o2 o3) (unary_morphism1_setoid1 o1 o2)
@@ -107,3 +114,4 @@ ndefinition comp_binary_morphisms:
  | #a; #a'; #b; #b'; #ea; #eb; #x; nnormalize;
    napply (.= †(eb x)); napply ea.
 nqed.
+*)