X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdatatypes%2Fcategories.ma;h=f5b23dfdd3a4fcbfc832edc89908eca62c3dacf1;hb=026c6c5b0e094b2e6e8244909bc5ac3d88b70b9c;hp=6dac9b044bb537175b1f4dc33708356563836fbc;hpb=e7cbfc078d4738277cf4a730c9407fc140bc029b;p=helm.git

diff --git a/helm/software/matita/library/datatypes/categories.ma b/helm/software/matita/library/datatypes/categories.ma
index 6dac9b044..f5b23dfdd 100644
--- a/helm/software/matita/library/datatypes/categories.ma
+++ b/helm/software/matita/library/datatypes/categories.ma
@@ -80,21 +80,14 @@ qed.
 coercion Leibniz.
 *)
 
-interpretation "setoid1 eq" 'eq x y = (eq_rel1 _ (eq1 _) x y).
-interpretation "setoid eq" 'eq x y = (eq_rel _ (eq _) x y).
+interpretation "setoid1 eq" 'eq t x y = (eq_rel1 _ (eq1 t) x y).
+interpretation "setoid eq" 'eq t x y = (eq_rel _ (eq t) x y).
 interpretation "setoid1 symmetry" 'invert r = (sym1 ____ r).
 interpretation "setoid symmetry" 'invert r = (sym ____ r).
 notation ".= r" with precedence 50 for @{'trans $r}.
 interpretation "trans1" 'trans r = (trans1 _____ r).
 interpretation "trans" 'trans r = (trans _____ r).
 
-(*
-record unary_morphism0 (A,B: setoid) : Type0 ≝
- { fun_0:1> A → B;
-   prop_0: ∀a,a'. eq ? a a' → eq ? (fun_0 a) (fun_0 a')
- }.
-*)
-
 record unary_morphism (A,B: setoid1) : Type0 ≝
  { fun_1:1> A → B;
    prop_1: ∀a,a'. eq1 ? a a' → eq1 ? (fun_1 a) (fun_1 a')
@@ -110,14 +103,10 @@ record binary_morphism1 (A,B,C:setoid1) : Type0 ≝
    prop1: ∀a,a',b,b'. eq1 ? a a' → eq1 ? b b' → eq1 ? (fun1 a b) (fun1 a' b')
  }.
 
-notation "hbox(a break ⇒ b)" right associative with precedence 20 for @{ 'Imply $a $b }.
-interpretation "unary morphism" 'Imply a b = (unary_morphism a b).
-
 notation "† c" with precedence 90 for @{'prop1 $c }.
 notation "l ‡ r" with precedence 90 for @{'prop $l $r }.
 notation "#" with precedence 90 for @{'refl}.
 interpretation "prop_1" 'prop1 c = (prop_1 _____ c).
-(* interpretation "prop_0" 'prop1 c = (prop_0 _____ c). *)
 interpretation "prop1" 'prop l r = (prop1 ________ l r).
 interpretation "prop" 'prop l r = (prop ________ l r).
 interpretation "refl1" 'refl = (refl1 ___).
@@ -217,3 +206,47 @@ interpretation "category1 composition" 'compose x y = (fun1 ___ (comp1 ____) y x
 interpretation "category1 assoc" 'assoc1 = (comp_assoc1 ________).
 interpretation "category composition" 'compose x y = (fun ___ (comp ____) y x).
 interpretation "category assoc" 'assoc = (comp_assoc ________).
+
+definition unary_morphism_setoid: setoid → setoid → setoid.
+ intros;
+ constructor 1;
+  [ apply (unary_morphism s s1);
+  | constructor 1;
+     [ intros (f g); apply (∀a. f a = g a);
+     | intros 1; simplify; intros; apply refl;
+     | simplify; intros; apply sym; apply H;
+     | simplify; intros; apply trans; [2: apply H; | skip | apply H1]]]
+qed.
+
+notation "hbox(a break ⇒ b)" right associative with precedence 20 for @{ 'Imply $a $b }.
+interpretation "unary morphism" 'Imply a b = (unary_morphism_setoid a b).
+interpretation "unary morphism" 'Imply a b = (unary_morphism a b).
+
+definition SET: category1.
+ constructor 1;
+  [ apply setoid;
+  | apply rule (λS,T.unary_morphism_setoid S T);
+  | intros; constructor 1; [ apply (λx.x); | intros; assumption ]
+  | intros; constructor 1; [ intros; constructor 1; [ apply (λx. c1 (c x)); | intros;
+     apply († (†H));]
+  | intros; whd; intros; simplify; whd in H1; whd in H;
+    apply trans; [ apply (b (a' a1)); | lapply (prop_1 ?? b (a a1) (a' a1));
+     [ apply Hletin | apply (H a1); ]  | apply H1; ]]
+  | intros; whd; intros; simplify; apply refl;
+  | intros; simplify; whd; intros; simplify; apply refl;
+  | intros; simplify; whd; intros; simplify; apply refl;
+  ]
+qed.
+
+definition setoid_OF_SET: objs1 SET → setoid.
+ intros; apply o; qed.
+
+coercion setoid_OF_SET.
+
+
+definition prop_1_SET : 
+ ∀A,B:SET.∀w:arrows1 SET A B.∀a,b:A.eq1 ? a b→eq1 ? (w a) (w b).
+intros; apply (prop_1 A B w a b H);
+qed.
+
+interpretation "SET dagger" 'prop1 h = (prop_1_SET _ _ _ _ _ h).