minor fixes

[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 7ac1b0b3d6d2f3b66a46c0fc3b4e49465d7aa4f2..3e750928d229ead63a7df26905c3a14a8b62830e 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/categories.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
@@ -14,6 +14,14 @@
 
 include "cprop_connectives.ma".
 
+notation "hvbox(a break = \sub \ID b)" non associative with precedence 45
+for @{ 'eqID $a $b }.
+
+notation > "hvbox(a break =_\ID b)" non associative with precedence 45
+for @{ cic:/matita/logic/equality/eq.ind#xpointer(1/1) ? $a $b }.
+
+interpretation "ID eq" 'eqID x y = (cic:/matita/logic/equality/eq.ind#xpointer(1/1) _ x y).
+
 record equivalence_relation (A:Type0) : Type1 ≝
  { eq_rel:2> A → A → CProp0;
    refl: reflexive ? eq_rel;
@@ -96,10 +104,22 @@ record setoid3: Type4 ≝
  }.
 
 
-interpretation "setoid3 eq" 'eq x y = (eq_rel3 _ (eq3 _) x y).
-interpretation "setoid2 eq" 'eq x y = (eq_rel2 _ (eq2 _) x y).
-interpretation "setoid1 eq" 'eq x y = (eq_rel1 _ (eq1 _) x y).
-interpretation "setoid eq" 'eq x y = (eq_rel _ (eq _) x y).
+interpretation "setoid3 eq" 'eq t x y = (eq_rel3 _ (eq3 t) x y).
+interpretation "setoid2 eq" 'eq t x y = (eq_rel2 _ (eq2 t) 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).
+
+notation > "hvbox(a break =_12 b)" non associative with precedence 45
+for @{ eq_rel2 (carr2 (setoid2_of_setoid1 ?)) (eq2 (setoid2_of_setoid1 ?)) $a $b }.
+notation > "hvbox(a break =_0 b)" non associative with precedence 45
+for @{ eq_rel ? (eq ?) $a $b }.
+notation > "hvbox(a break =_1 b)" non associative with precedence 45
+for @{ eq_rel1 ? (eq1 ?) $a $b }.
+notation > "hvbox(a break =_2 b)" non associative with precedence 45
+for @{ eq_rel2 ? (eq2 ?) $a $b }.
+notation > "hvbox(a break =_3 b)" non associative with precedence 45
+for @{ eq_rel3 ? (eq3 ?) $a $b }.
+
 interpretation "setoid3 symmetry" 'invert r = (sym3 ____ r).
 interpretation "setoid2 symmetry" 'invert r = (sym2 ____ r).
 interpretation "setoid1 symmetry" 'invert r = (sym1 ____ r).
@@ -302,9 +322,8 @@ record functor2 (C1: category2) (C2: category2) : Type3 ≝
    map_arrows2: ∀S,T. unary_morphism2 (arrows2 ? S T) (arrows2 ? (map_objs2 S) (map_objs2 T));
    respects_id2: ∀o:C1. map_arrows2 ?? (id2 ? o) = id2 ? (map_objs2 o);
    respects_comp2:
-     ∀o1,o2,o3,o4.∀f1:arrows2 ? o1 o2.∀f2:arrows2 ? o2 o3.∀f3:arrows2 ? o3 o4.
-     map_arrows2 ?? (f3 ∘ f2 ∘ f1) =
-      map_arrows2 ?? f3 ∘ map_arrows2 ?? f2 ∘ map_arrows2 ?? f1}.
+     ∀o1,o2,o3.∀f1:arrows2 ? o1 o2.∀f2:arrows2 ? o2 o3.
+     map_arrows2 ?? (f2 ∘ f1) = map_arrows2 ?? f2 ∘ map_arrows2 ?? f1}.
 
 definition functor2_setoid: category2 → category2 → setoid3.
  intros (C1 C2);
@@ -443,4 +462,4 @@ coercion objs2_of_category1.
 prefer coercion Type_OF_setoid. (* we prefer the lower carrier projection *)
 prefer coercion Type_OF_objs1.
 
-interpretation "unary morphism1" 'Imply a b = (arrows2 SET1 a b).
\ No newline at end of file
+interpretation "unary morphism1" 'Imply a b = (arrows2 SET1 a b).