From 1434d54f86fcce0296bcda49086ce7f7040aa53d Mon Sep 17 00:00:00 2001
From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Sun, 13 Sep 2009 21:02:15 +0000
Subject: [PATCH] a nice bug in meta handling is not visible... brr...

---
 .../software/matita/nlibrary/topology/igft.ma | 94 +++----------------
 1 file changed, 12 insertions(+), 82 deletions(-)

diff --git a/helm/software/matita/nlibrary/topology/igft.ma b/helm/software/matita/nlibrary/topology/igft.ma
index 9bff8502f..b3f2c2d6b 100644
--- a/helm/software/matita/nlibrary/topology/igft.ma
+++ b/helm/software/matita/nlibrary/topology/igft.ma
@@ -6,6 +6,12 @@ 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 }.
+
+interpretation "I" 'I a = (I ? a).
+interpretation "C" 'C a i = (C ? a i).
+
 ndefinition cover_set ≝ λc:∀A:axiom_set.Ω^A → A → CProp[0].λA,C,U.
   ∀y.y ∈ C → c A U y.
 
@@ -17,7 +23,7 @@ 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:I ? a. (C ? a i ◃ U) → cover ? U a.
+| cinfinity    : ∀a:A. ∀i:?. ((C ? a i) ◃ U) → cover ? U a.
 napply cover;
 nqed.
 
@@ -35,7 +41,7 @@ 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 a i ⋉ F) → fish A F a.
 napply fish;
 nqed.
 
@@ -44,7 +50,7 @@ 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;
@@ -61,7 +67,7 @@ ndefinition coverage : ∀A:axiom_set.∀U:Ω^A.Ω^A ≝ λA,U.{ a | a ◃ U }.
 interpretation "coverage cover" 'coverage U = (coverage ? U).
 
 ndefinition cover_equation : ∀A:axiom_set.∀U,X:Ω^A.CProp[0] ≝  λA,U,X. 
-  ∀a.a ∈ X ↔ (a ∈ U ∨ ∃i:I ? a.∀y.y ∈ C ? a i → y ∈ X).  
+  ∀a.a ∈ X ↔ (a ∈ U ∨ ∃i:𝐈 a.∀y.y ∈ 𝐂 a i → y ∈ X).  
 
 ntheorem coverage_cover_equation : ∀A,U. cover_equation A U (◃U).
 #A; #U; #a; @; #H;
@@ -90,7 +96,7 @@ ndefinition fished : ∀A:axiom_set.∀F:Ω^A.Ω^A ≝ λA,F.{ a | a ⋉ F }.
 interpretation "fished fish" 'fished F = (fished ? F).
 
 ndefinition fish_equation : ∀A:axiom_set.∀F,X:Ω^A.CProp[0] ≝ λA,F,X.
-  ∀a. a ∈ X ↔ a ∈ F ∧ ∀i:I ? a.∃y.y ∈ C ? a i ∧ y ∈ X. 
+  ∀a. a ∈ X ↔ a ∈ F ∧ ∀i:𝐈 a.∃y.y ∈ 𝐂 a i ∧ y ∈ X. 
   
 ntheorem fised_fish_equation : ∀A,F. fish_equation A F (⋉F).
 #A; #F; #a; @; (* bug, fare case sotto diverso da farlo sopra *) #H; ncases H;
@@ -100,84 +106,8 @@ ntheorem fised_fish_equation : ∀A,F. fish_equation A F (⋉F).
 ##]
 nqed.
 
-ntheorem fised_min_fish_equation : ∀A,F,G. fish_equation A F G → G ⊆ ⋉F.
+ntheorem fised_max_fish_equation : ∀A,F,G. fish_equation A F G → G ⊆ ⋉F.
 #A; #F; #G; #H; #a; #aG; napply (fish_rec … aG);
 #b; ncases (H b); #H1; #_; #bG; ncases (H1 bG); #E1; #E2; nassumption; 
 nqed. 
 
-STOP
-
-(*
-alias symbol "covers" (instance 0) = "covers".
-alias symbol "covers" (instance 2) = "covers".
-alias symbol "covers" (instance 1) = "covers set".
-ntheorem covers_elim2:
- ∀A: axiom_set. ∀U:Ω^A.∀P: A → CProp[0].
-  (∀a:A. a ∈ U → P a) →
-   (∀a:A.∀V:Ω^A. a ◃ V → V ◃ U → (∀y. y ∈ V → P y) → P a) →
-     ∀a:A. a ◃ U → P a.
-#A; #U; #P; #H1; #H2; #a; #aU; nelim aU;
-##[ #b; #H; napply H1; napply H;
-##| #b; #i; #CaiU; #H; napply H2; 
-    ##[ napply (C ? b i);
-    ##| napply cinfinity; ##[ napply i ] nwhd; #y; #H3; napply creflexivity; ##]
-    nassumption; 
-##]
-nqed.
-*)
-
-alias symbol "fish" (instance 1) = "fish set".
-alias symbol "covers" = "covers".
-ntheorem compatibility: ∀A:axiom_set.∀a:A.∀U,V. a ⋉ V → a ◃ U → U ⋉ V.
-#A; #a; #U; #V; #aV; #aU; ngeneralize in match aV; (* clear aV *)
-nelim aU;
-##[ #b; #bU; #bV; @; ##[ napply b] @; nassumption;
-##| #b; #i; #CaiU; #H; #bV; ncases bV in i CaiU H;
-    #c; #cV; #CciV; #i; #CciU; #H; ncases (CciV i); #x; *; #xCci; #xV;
-    napply H; nassumption;
-##]
-nqed.
-
-
-
-
-STOP
-
-definition leq ≝ λA:axiom_set.λa,b:A. a ◃ {y|b=y}.
-
-interpretation "covered by one" 'leq a b = (leq ? a b).
-
-theorem leq_refl: ∀A:axiom_set.∀a:A. a ≤ a.
- intros;
- apply refl;
- normalize;
- reflexivity.
-qed.
-
-theorem leq_trans: ∀A:axiom_set.∀a,b,c:A. a ≤ b → b ≤ c → a ≤ c.
- intros;
- unfold in H H1 ⊢ %;
- apply (transitivity ???? H);
- constructor 1;
- intros;
- normalize in H2;
- rewrite < H2;
- assumption.
-qed.
-
-definition uparrow ≝ λA:axiom_set.λa:A.mk_powerset ? (λb:A. a ≤ b).
-
-interpretation "uparrow" 'uparrow a = (uparrow ? a).
-
-definition downarrow ≝ λA:axiom_set.λU:Ω \sup A.mk_powerset ? (λa:A. (↑a) ≬ U).
-
-interpretation "downarrow" 'downarrow a = (downarrow ? a).
-
-definition fintersects ≝ λA:axiom_set.λU,V:Ω \sup A.↓U ∩ ↓V.
-
-interpretation "fintersects" 'fintersects U V = (fintersects ? U V).
-
-record convergent_generated_topology : Type ≝
- { AA:> axiom_set;
-   convergence: ∀a:AA.∀U,V:Ω \sup AA. a ◃ U → a ◃ V → a ◃ (U ↓ V)
- }.
-- 
2.39.2