update in groud_2 and models

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

diff --git a/helm/software/matita/nlibrary/sets/categories.ma b/helm/software/matita/nlibrary/sets/categories.ma
index 38c8129fa28d3d7dc0a55a5d51a588102f284d66..6d57deddb02d493a2e6c3b8a0d178a5ce01cac14 100644 (file)
--- a/helm/software/matita/nlibrary/sets/categories.ma
+++ b/helm/software/matita/nlibrary/sets/categories.ma
@@ -26,10 +26,6 @@ nrecord category : Type[2] ≝
    id_neutral_right: ∀o1,o2. ∀a: arrows o1 o2. comp ??? a (id o1) = a
  }.
 
-notation "hvbox(A break ⇒ B)" right associative with precedence 50 for @{ 'arrows $A $B }.
-interpretation "arrows1" 'arrows A B = (unary_morphism1 A B).
-interpretation "arrows" 'arrows A B = (unary_morphism A B).
-
 notation > "𝐈𝐝 term 90 A" non associative with precedence 90 for @{ 'id $A }.
 notation < "mpadded width -90% (𝐈) 𝐝 \sub term 90 A" non associative with precedence 90 for @{ 'id $A }.
 
@@ -69,7 +65,7 @@ ndefinition TYPE : setoid1.
 @ setoid; @; 
 ##[ #T1; #T2; 
     alias symbol "eq" = "setoid eq".
-    napply (∃f:T1 ⇒ T2.∃g:T2 ⇒ T1. (∀x.f (g x) = x) ∧ (∀y.g (f y) = y));
+    napply (∃f:T1 ⇒_0 T2.∃g:T2 ⇒_0 T1. (∀x.f (g x) = x) ∧ (∀y.g (f y) = y));
 ##| #A; @ (𝐈𝐝 A); @ (𝐈𝐝 A); @; #x; napply #;
 ##| #A; #B; *; #f; *; #g; *; #Hfg; #Hgf; @g; @f; @; nassumption; 
 ##| #A; #B; #C; *; #f; *; #f'; *; #Hf; #Hf'; *; #g; *; #g'; *; #Hg; #Hg'; 
@@ -87,7 +83,7 @@ unification hint 0 ≔ ;
    
 nrecord unary_morphism01 (A : setoid) (B: setoid1) : Type[1] ≝
  { fun01:1> A → B;
-   prop01: ∀a,a'. eq ? a a' → eq1 ? (fun01 a) (fun01 a')
+   prop01: ∀a,a'. eq0 ? a a' → eq1 ? (fun01 a) (fun01 a')
  }.
  
 interpretation "prop01" 'prop1 c  = (prop01 ????? c).