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[helm.git] / helm / software / matita / contribs / formal_topology / overlap / categories.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/categories.ma b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
index ea246ef6c8e501c58a50b571763ccb50ee693812..86bc2529cda85de608a0ab1087396d277af75efe 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/categories.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
@@ -181,6 +181,7 @@ interpretation "prop11" 'prop1 c = (prop11 _____ c).
 interpretation "prop12" 'prop1 c = (prop12 _____ c).
 interpretation "prop2" 'prop2 l r = (prop2 ________ l r).
 interpretation "prop21" 'prop2 l r = (prop21 ________ l r).
+interpretation "prop22" 'prop2 l r = (prop22 ________ l r).
 interpretation "refl" 'refl = (refl ___).
 interpretation "refl1" 'refl = (refl1 ___).
 interpretation "refl2" 'refl = (refl2 ___).
@@ -285,13 +286,11 @@ record category2 : Type3 ≝
  }.
 
 notation "'ASSOC'" with precedence 90 for @{'assoc}.
-notation "'ASSOC1'" with precedence 90 for @{'assoc1}.
-notation "'ASSOC2'" with precedence 90 for @{'assoc2}.
 
-interpretation "category1 composition" 'compose x y = (fun22 ___ (comp2 ____) y x).
-interpretation "category1 assoc" 'assoc1 = (comp_assoc2 ________).
+interpretation "category2 composition" 'compose x y = (fun22 ___ (comp2 ____) y x).
+interpretation "category2 assoc" 'assoc = (comp_assoc2 ________).
 interpretation "category1 composition" 'compose x y = (fun21 ___ (comp1 ____) y x).
-interpretation "category1 assoc" 'assoc1 = (comp_assoc1 ________).
+interpretation "category1 assoc" 'assoc = (comp_assoc1 ________).
 interpretation "category composition" 'compose x y = (fun2 ___ (comp ____) y x).
 interpretation "category assoc" 'assoc = (comp_assoc ________).
 
@@ -387,11 +386,24 @@ definition prop11_SET1 :
 intros; apply (prop11 A B w a b e);
 qed.
 
-definition hint: Type_OF_category2 SET1 → Type1.
+definition setoid2_OF_category2: Type_OF_category2 SET1 → setoid2.
+ intro; apply (setoid2_of_setoid1 t); qed.
+coercion setoid2_OF_category2.
+
+definition objs2_OF_category1: Type_OF_category1 SET → objs2 SET1.
+ intro; apply (setoid1_of_setoid t); qed.
+coercion objs2_OF_category1.
+
+definition Type1_OF_SET1: Type_OF_category2 SET1 → Type1.
  intro; whd in t; apply (carr1 t);
 qed.
-coercion hint.
+coercion Type1_OF_SET1.
 
 interpretation "SET dagger" 'prop1 h = (prop11_SET1 _ _ _ _ _ h).
 interpretation "unary morphism1" 'Imply a b = (arrows2 SET1 a b).
 interpretation "SET1 eq" 'eq x y = (eq_rel1 _ (eq'' _) x y).
+
+lemma unary_morphism1_of_arrows1_SET1: ∀S,T. (S ⇒ T) → unary_morphism1 S T.
+ intros; apply t;
+qed.
+coercion unary_morphism1_of_arrows1_SET1.