...

[helm.git] / helm / software / matita / library / datatypes / categories.ma

diff --git a/helm/software/matita/library/datatypes/categories.ma b/helm/software/matita/library/datatypes/categories.ma
index ca49cbdd327f2909da9a3fca5b7e9ce8bbf39730..f5b23dfdd3a4fcbfc832edc89908eca62c3dacf1 100644 (file)
--- a/helm/software/matita/library/datatypes/categories.ma
+++ b/helm/software/matita/library/datatypes/categories.ma
@@ -80,8 +80,8 @@ 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}.
@@ -236,4 +236,17 @@ definition SET: category1.
   | intros; simplify; whd; intros; simplify; apply refl;
   | intros; simplify; whd; intros; simplify; apply refl;
   ]
-qed.
\ No newline at end of file
+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).