more notation for topologies, and some prentheses that can be used in notation

[helm.git] / helm / software / matita / nlibrary / topology / igft.ma

diff --git a/helm/software/matita/nlibrary/topology/igft.ma b/helm/software/matita/nlibrary/topology/igft.ma
index b3f2c2d6b1ea10781a62e75b729e8474d06d2db7..c009f2464f07665c1515ac0577aeca30ae148835 100644 (file)
--- a/helm/software/matita/nlibrary/topology/igft.ma
+++ b/helm/software/matita/nlibrary/topology/igft.ma
@@ -6,8 +6,11 @@ nrecord axiom_set : Type[1] ≝ {
   C: ∀a:S. I a → Ω ^ S
 }.
 
-notation "𝐈 term 90 a" non associative with precedence 70 for @{ 'I $a }.
-notation "𝐂 term 90 a term 90 i" non associative with precedence 70 for @{ 'C $a $i }.
+notation "𝐈  \sub( ❨term 90 a❩ )" non associative with precedence 70 for @{ 'I $a }.
+notation "𝐂 \sub ( ❨term 90 a,\emsp term 90 i❩ )" non associative with precedence 70 for @{ 'C $a $i }.
+
+notation > "𝐈 term 90 a" non associative with precedence 70 for @{ 'I $a }.
+notation > "𝐂 term 90 a term 90 i" non associative with precedence 70 for @{ 'C $a $i }.
 
 interpretation "I" 'I a = (I ? a).
 interpretation "C" 'C a i = (C ? a i).
@@ -23,7 +26,7 @@ interpretation "covers set temp" 'covers C U = (cover_set ?? C U).
 
 ninductive cover (A : axiom_set) (U : Ω^A) : A → CProp[0] ≝ 
 | creflexivity : ∀a:A. a ∈ U → cover ? U a
-| cinfinity    : ∀a:A. ∀i:?. ((C ? a i) ◃ U) → cover ? U a.
+| cinfinity    : ∀a:A.∀i:𝐈 a. 𝐂 a i ◃ U → cover ? U a.
 napply cover;
 nqed.
 
@@ -41,7 +44,7 @@ for @{ 'fish $a $b }.
 interpretation "fish set temp" 'fish A U = (fish_set ?? U A).
 
 ncoinductive fish (A : axiom_set) (F : Ω^A) : A → CProp[0] ≝ 
-| cfish : ∀a. a ∈ F → (∀i:𝐈 a.C A a i ⋉ F) → fish A F a.
+| cfish : ∀a. a ∈ F → (∀i:𝐈 a .𝐂  a i ⋉ F) → fish A F a.
 napply fish;
 nqed.
 
@@ -50,7 +53,7 @@ interpretation "fish" 'fish a U = (fish ? U a).
 
 nlet corec fish_rec (A:axiom_set) (U: Ω^A)
  (P: Ω^A) (H1: P ⊆ U)
-  (H2: ∀a:A. a ∈ P → ∀j: 𝐈 a. C ? a j ≬ P):
+  (H2: ∀a:A. a ∈ P → ∀j: 𝐈 a. 𝐂 a j ≬ P):
    ∀a:A. ∀p: a ∈ P. a ⋉ U ≝ ?.
 #a; #p; napply cfish;
 ##[ napply H1; napply p;
@@ -81,7 +84,8 @@ ntheorem coverage_cover_equation : ∀A,U. cover_equation A U (◃U).
 ##]
 nqed. 
 
-ntheorem coverage_min_cover_equation : ∀A,U,W. cover_equation A U W → ◃U ⊆ W.
+ntheorem coverage_min_cover_equation : 
+  ∀A,U,W. cover_equation A U W → ◃U ⊆ W.
 #A; #U; #W; #H; #a; #aU; nelim aU; #b;
 ##[ #bU; ncases (H b); #_; #H1; napply H1; @1; nassumption;
 ##| #i; #CbiU; #IH; ncases (H b); #_; #H1; napply H1; @2; @i; napply IH;