X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fdatatypes%2Fcategories.ma;h=b9e365c7e53d0e98ed01ac6f12ddea099d577081;hb=fc1e871dde0f9f4cfde6f4a4fda8d18022584e65;hp=ca49cbdd327f2909da9a3fca5b7e9ce8bbf39730;hpb=87ff605d8efbc7d5ca7b89cdb6bf04f0a2ddf489;p=helm.git

diff --git a/helm/software/matita/library/datatypes/categories.ma b/helm/software/matita/library/datatypes/categories.ma
index ca49cbdd3..b9e365c7e 100644
--- a/helm/software/matita/library/datatypes/categories.ma
+++ b/helm/software/matita/library/datatypes/categories.ma
@@ -80,13 +80,13 @@ 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 symmetry" 'invert r = (sym1 ____ r).
-interpretation "setoid symmetry" 'invert r = (sym ____ r).
+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).
+interpretation "trans1" 'trans r = (trans1 ????? r).
+interpretation "trans" 'trans r = (trans ????? r).
 
 record unary_morphism (A,B: setoid1) : Type0 ≝
  { fun_1:1> A → B;
@@ -106,11 +106,11 @@ record binary_morphism1 (A,B,C:setoid1) : Type0 ≝
 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 "prop1" 'prop l r = (prop1 ________ l r).
-interpretation "prop" 'prop l r = (prop ________ l r).
-interpretation "refl1" 'refl = (refl1 ___).
-interpretation "refl" 'refl = (refl ___).
+interpretation "prop_1" 'prop1 c = (prop_1 ????? c).
+interpretation "prop1" 'prop l r = (prop1 ???????? l r).
+interpretation "prop" 'prop l r = (prop ???????? l r).
+interpretation "refl1" 'refl = (refl1 ???).
+interpretation "refl" 'refl = (refl ???).
 
 definition CPROP: setoid1.
  constructor 1;
@@ -128,7 +128,7 @@ definition if': ∀A,B:CPROP. A = B → A → B.
 qed.
 
 notation ". r" with precedence 50 for @{'if $r}.
-interpretation "if" 'if r = (if' __ r).
+interpretation "if" 'if r = (if' ?? r).
 
 definition and_morphism: binary_morphism1 CPROP CPROP CPROP.
  constructor 1;
@@ -140,7 +140,7 @@ definition and_morphism: binary_morphism1 CPROP CPROP CPROP.
      | apply (fi ?? H1 b1)]]
 qed.
 
-interpretation "and_morphism" 'and a b = (fun1 ___ and_morphism a b).
+interpretation "and_morphism" 'and a b = (fun1 ??? and_morphism a b).
 
 definition or_morphism: binary_morphism1 CPROP CPROP CPROP.
  constructor 1;
@@ -152,7 +152,7 @@ definition or_morphism: binary_morphism1 CPROP CPROP CPROP.
      | apply (fi ?? H1 b1)]]
 qed.
 
-interpretation "or_morphism" 'or a b = (fun1 ___ or_morphism a b).
+interpretation "or_morphism" 'or a b = (fun1 ??? or_morphism a b).
 
 definition if_morphism: binary_morphism1 CPROP CPROP CPROP.
  constructor 1;
@@ -202,10 +202,10 @@ record category1 : Type2 ≝
 notation "'ASSOC'" with precedence 90 for @{'assoc}.
 notation "'ASSOC1'" with precedence 90 for @{'assoc1}.
 
-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 ________).
+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;
@@ -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).