X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fformal_topology%2Foverlap%2Fcategories.ma;h=30a8159fb911e57a20314fcc1ff66376b66e2857;hb=a88be1ca42c0969dbab9a5c76240f5931df876d9;hp=7ac1b0b3d6d2f3b66a46c0fc3b4e49465d7aa4f2;hpb=4bdb34a1cce33b4387b04cc37bf229e08f5bbafb;p=helm.git

diff --git a/helm/software/matita/contribs/formal_topology/overlap/categories.ma b/helm/software/matita/contribs/formal_topology/overlap/categories.ma
index 7ac1b0b3d..30a8159fb 100644
--- 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;
@@ -80,7 +88,7 @@ qed.
 coercion setoid2_of_setoid1.
 prefer coercion Type_OF_setoid2. 
 prefer coercion Type_OF_setoid. 
-prefer coercion Type_OF_setoid1. 
+prefer coercion Type_OF_setoid1.
 (* we prefer 0 < 1 < 2 *)
 
 record equivalence_relation3 (A:Type3) : Type4 ≝
@@ -96,19 +104,31 @@ 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 symmetry" 'invert r = (sym3 ____ r).
-interpretation "setoid2 symmetry" 'invert r = (sym2 ____ r).
-interpretation "setoid1 symmetry" 'invert r = (sym1 ____ r).
-interpretation "setoid symmetry" 'invert r = (sym ____ r).
+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).
+interpretation "setoid symmetry" 'invert r = (sym ???? r).
 notation ".= r" with precedence 50 for @{'trans $r}.
-interpretation "trans3" 'trans r = (trans3 _____ r).
-interpretation "trans2" 'trans r = (trans2 _____ r).
-interpretation "trans1" 'trans r = (trans1 _____ r).
-interpretation "trans" 'trans r = (trans _____ r).
+interpretation "trans3" 'trans r = (trans3 ????? r).
+interpretation "trans2" 'trans r = (trans2 ????? r).
+interpretation "trans1" 'trans r = (trans1 ????? r).
+interpretation "trans" 'trans r = (trans ????? r).
 
 record unary_morphism (A,B: setoid) : Type0 ≝
  { fun1:1> A → B;
@@ -153,20 +173,21 @@ record binary_morphism3 (A,B,C:setoid3) : Type3 ≝
 notation "† c" with precedence 90 for @{'prop1 $c }.
 notation "l ‡ r" with precedence 90 for @{'prop2 $l $r }.
 notation "#" with precedence 90 for @{'refl}.
-interpretation "prop1" 'prop1 c  = (prop1 _____ c).
-interpretation "prop11" 'prop1 c = (prop11 _____ c).
-interpretation "prop12" 'prop1 c = (prop12 _____ c).
-interpretation "prop13" 'prop1 c = (prop13 _____ 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 "prop23" 'prop2 l r = (prop23 ________ l r).
-interpretation "refl" 'refl = (refl ___).
-interpretation "refl1" 'refl = (refl1 ___).
-interpretation "refl2" 'refl = (refl2 ___).
-interpretation "refl3" 'refl = (refl3 ___).
-
-definition unary_morphism2_of_unary_morphism1: ∀S,T.unary_morphism1 S T → unary_morphism2 S T.
+interpretation "prop1" 'prop1 c  = (prop1 ????? c).
+interpretation "prop11" 'prop1 c = (prop11 ????? c).
+interpretation "prop12" 'prop1 c = (prop12 ????? c).
+interpretation "prop13" 'prop1 c = (prop13 ????? 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 "prop23" 'prop2 l r = (prop23 ???????? l r).
+interpretation "refl" 'refl = (refl ???).
+interpretation "refl1" 'refl = (refl1 ???).
+interpretation "refl2" 'refl = (refl2 ???).
+interpretation "refl3" 'refl = (refl3 ???).
+
+definition unary_morphism2_of_unary_morphism1: 
+  ∀S,T:setoid1.unary_morphism1 S T → unary_morphism2 (setoid2_of_setoid1 S) T.
  intros;
  constructor 1;
   [ apply (fun11 ?? u);
@@ -193,7 +214,7 @@ definition fi': ∀A,B:CPROP. A = B → B → A.
 qed.
 
 notation ". r" with precedence 50 for @{'fi $r}.
-interpretation "fi" 'fi r = (fi' __ r).
+interpretation "fi" 'fi r = (fi' ?? r).
 
 definition and_morphism: binary_morphism1 CPROP CPROP CPROP.
  constructor 1;
@@ -205,7 +226,7 @@ definition and_morphism: binary_morphism1 CPROP CPROP CPROP.
      | apply (fi ?? e1 b1)]]
 qed.
 
-interpretation "and_morphism" 'and a b = (fun21 ___ and_morphism a b).
+interpretation "and_morphism" 'and a b = (fun21 ??? and_morphism a b).
 
 definition or_morphism: binary_morphism1 CPROP CPROP CPROP.
  constructor 1;
@@ -217,7 +238,7 @@ definition or_morphism: binary_morphism1 CPROP CPROP CPROP.
      | apply (fi ?? e1 b1)]]
 qed.
 
-interpretation "or_morphism" 'or a b = (fun21 ___ or_morphism a b).
+interpretation "or_morphism" 'or a b = (fun21 ??? or_morphism a b).
 
 definition if_morphism: binary_morphism1 CPROP CPROP CPROP.
  constructor 1;
@@ -274,12 +295,12 @@ record category3 : Type4 ≝
 
 notation "'ASSOC'" with precedence 90 for @{'assoc}.
 
-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" 'assoc = (comp_assoc1 ________).
-interpretation "category composition" 'compose x y = (fun2 ___ (comp ____) y x).
-interpretation "category assoc" 'assoc = (comp_assoc ________).
+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" 'assoc = (comp_assoc1 ????????).
+interpretation "category composition" 'compose x y = (fun2 ??? (comp ????) y x).
+interpretation "category assoc" 'assoc = (comp_assoc ????????).
 
 definition category2_of_category1: category1 → category2.
  intro;
@@ -302,9 +323,8 @@ 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 +463,4 @@ 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).