From 90d29632ac1705a0d217d54623a63fdf6f013e28 Mon Sep 17 00:00:00 2001
From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Thu, 10 Sep 2009 14:45:46 +0000
Subject: [PATCH] it starts to work

---
 helm/software/matita/nlibrary/sets/sets.ma    | 70 +++++++++----------
 .../software/matita/nlibrary/topology/igft.ma |  2 +-
 2 files changed, 36 insertions(+), 36 deletions(-)

diff --git a/helm/software/matita/nlibrary/sets/sets.ma b/helm/software/matita/nlibrary/sets/sets.ma
index 348332441..8553c0fd1 100644
--- a/helm/software/matita/nlibrary/sets/sets.ma
+++ b/helm/software/matita/nlibrary/sets/sets.ma
@@ -28,30 +28,30 @@ interpretation "subseteq" 'subseteq U V = (subseteq ? U V).
 ndefinition overlaps ≝ λA.λU,V.∃x:A.x ∈ U ∧ x ∈ V.
 interpretation "overlaps" 'overlaps U V = (overlaps ? U V).
 
-ndefinition intersect ≝ λA.λU,V:Ω \sup A.{ x | x ∈ U ∧ x ∈ V }.
+ndefinition intersect ≝ λA.λU,V:Ω^A.{ x | x ∈ U ∧ x ∈ V }.
 interpretation "intersect" 'intersects U V = (intersect ? U V).
 
-ndefinition union ≝ λA.λU,V:Ω \sup A.{ x | x ∈ U ∨ x ∈ V }.
+ndefinition union ≝ λA.λU,V:Ω^A.{ x | x ∈ U ∨ x ∈ V }.
 interpretation "union" 'union U V = (union ? U V).
 
-ndefinition big_union ≝ λA,B.λT:Ω \sup A.λf:A → Ω \sup B.{ x | ∃i. i ∈ T ∧ x ∈ f i }.
+ndefinition big_union ≝ λA,B.λT:Ω^A.λf:A → Ω^B.{ x | ∃i. i ∈ T ∧ x ∈ f i }.
 
-ndefinition big_intersection ≝ λA,B.λT:Ω \sup A.λf:A → Ω \sup B.{ x | ∀i. i ∈ T → x ∈ f i }.
+ndefinition big_intersection ≝ λA,B.λT:Ω^A.λf:A → Ω^B.{ x | ∀i. i ∈ T → x ∈ f i }.
 
-ndefinition full_set: ∀A. Ω \sup A ≝ λA.{ x | True }.
-ncoercion full_set : ∀A:Type[0]. Ω \sup A ≝ full_set on A: Type[0] to (Ω \sup ?).
+ndefinition full_set: ∀A. Ω^A ≝ λA.{ x | True }.
+ncoercion full_set : ∀A:Type[0]. Ω^A ≝ full_set on A: Type[0] to (Ω^?).
 
-nlemma subseteq_refl: ∀A.∀S: Ω \sup A. S ⊆ S.
+nlemma subseteq_refl: ∀A.∀S: Ω^A. S ⊆ S.
  #A; #S; #x; #H; nassumption.
 nqed.
 
-nlemma subseteq_trans: ∀A.∀S,T,U: Ω \sup A. S ⊆ T → T ⊆ U → S ⊆ U.
+nlemma subseteq_trans: ∀A.∀S,T,U: Ω^A. S ⊆ T → T ⊆ U → S ⊆ U.
  #A; #S; #T; #U; #H1; #H2; #x; #P; napply H2; napply H1; nassumption.
 nqed.
 
 include "properties/relations1.ma".
 
-ndefinition seteq: ∀A. equivalence_relation1 (Ω \sup A).
+ndefinition seteq: ∀A. equivalence_relation1 (Ω^A).
  #A; napply mk_equivalence_relation1
   [ napply (λS,S'. S ⊆ S' ∧ S' ⊆ S)
   | #S; napply conj; napply subseteq_refl
@@ -104,7 +104,8 @@ ndefinition qpowerclass_setoid: setoid → setoid1.
   | napply (qseteq A) ]
 nqed.
 
-unification hint 0 ≔ A : ? ⊢  carr1 (qpowerclass_setoid A) ≡ qpowerclass A.
+unification hint 0 ≔ A : ? ⊢  
+  carr1 (qpowerclass_setoid A) ≡ qpowerclass A.
 
 nlemma mem_ok: ∀A. binary_morphism1 (setoid1_of_setoid A) (qpowerclass_setoid A) CPROP.
  #A; napply mk_binary_morphism1
@@ -145,37 +146,34 @@ nqed.
 alias symbol "hint_decl" = "hint_decl_Type1".
 unification hint 0 ≔ 
   A : setoid, B : qpowerclass A, C : qpowerclass A ⊢ 
-    pc A (fun21 ???  (intersect_ok A) B C) ≡ intersect ? (pc ? B) (pc ? C).
+    pc A (intersect_ok A B C) ≡ intersect ? (pc ? B) (pc ? C).
 
-(* hints can pass under mem *)
-unification hint 0 ( 
-  ∀A,B,x.
-   let C ≝ B in 
-    (λa,b.Prop) (mem A B x) (mem A C x)).
+(* hints can pass under mem *) (* ??? XXX why is it needed? *)
+unification hint 0 ≔ A:?, B:?, x:?;
+           C ≟ B
+ (*---------------------*) ⊢ 
+   mem A B x ≡ mem A C x.
 
 nlemma test: ∀A:setoid. ∀U,V:qpowerclass A. ∀x,x':setoid1_of_setoid A. x=x' → x ∈ U ∩ V → x' ∈ U ∩ V.
  #A; #U; #V; #x; #x'; #H; #p; napply (. (H^-1‡#)); nassumption.
 nqed.
 
-(*
-(* qui non funziona una cippa *)
-ndefinition image: ∀A,B. (carr A → carr B) → Ω \sup A → Ω \sup B ≝
- λA,B:setoid.λf:carr A → carr B.λSa:Ω \sup A.
-  {y | ∃x. x ∈ Sa ∧ eq_rel (carr B) (eq B) ? ?(*(f x) y*)}.
-  ##[##2: napply (f x); ##|##3: napply y]
- #a; #a'; #H; nwhd; nnormalize; (* per togliere setoid1_of_setoid *) napply (mk_iff ????);
- *; #x; #Hx; napply (ex_intro … x)
-  [ napply (. (#‡(#‡#))); 
+ndefinition image: ∀A,B. (carr A → carr B) → Ω^A → Ω^B ≝
+ λA,B:setoid.λf:carr A → carr B.λSa:Ω^A.
+  {y | ∃x. x ∈ Sa ∧ eq_rel (carr B) (eq B) (f x) y}.
 
-ndefinition counter_image: ∀A,B. (A → B) → Ω \sup B → Ω \sup A ≝
+ndefinition counter_image: ∀A,B. (carr A → carr B) → Ω^B → Ω^A ≝
  λA,B,f,Sb. {x | ∃y. y ∈ Sb ∧ f x = y}.
-*)
 
 (******************* compatible equivalence relations **********************)
 
 nrecord compatible_equivalence_relation (A: setoid) : Type[1] ≝
  { rel:> equivalence_relation A;
-   compatibility: ∀x,x':A. x=x' → eq_rel ? rel x x' (* coercion qui non va *)
+   compatibility: ∀x,x':A. x=x' → rel x x'
+    (* coercion qui non andava per via di un Failure invece di Uncertain
+       ritornato dall'unificazione per il problema: 
+         ?[] A =?= ?[Γ]->?[Γ+1] 
+    *)
  }.
 
 ndefinition quotient: ∀A. compatible_equivalence_relation A → setoid.
@@ -197,19 +195,19 @@ nqed.
 
 ndefinition canonical_proj: ∀A,R. unary_morphism A (quotient A R).
  #A; #R; napply mk_unary_morphism
-  [ napply (λx.x) | #a; #a'; #H; napply (compatibility ? R … H) ]
+  [ napply (λx.x) | #a; #a'; #H; napply (compatibility … R … H) ]
 nqed.
 
 ndefinition quotiented_mor:
  ∀A,B.∀f:unary_morphism A B.
-  unary_morphism (quotient ? (eqrel_of_morphism ?? f)) B.
+  unary_morphism (quotient … (eqrel_of_morphism … f)) B.
  #A; #B; #f; napply mk_unary_morphism
   [ napply f | #a; #a'; #H; nassumption]
 nqed.
 
 nlemma first_omomorphism_theorem_functions1:
  ∀A,B.∀f: unary_morphism A B.
-  ∀x. f x = quotiented_mor ??? (canonical_proj ? (eqrel_of_morphism ?? f) x).
+  ∀x. f x = quotiented_mor … (canonical_proj … (eqrel_of_morphism … f) x).
  #A; #B; #f; #x; napply refl;
 nqed.
 
@@ -222,19 +220,21 @@ ndefinition injective ≝
   ∀x,x'. x ∈ S → x' ∈ S → f x = f x' → x = x'.
 
 nlemma first_omomorphism_theorem_functions2:
- ∀A,B.∀f: unary_morphism A B. surjective ?? (Full_set ?) (Full_set ?) (canonical_proj ? (eqrel_of_morphism ?? f)).
+ ∀A,B.∀f: unary_morphism A B. 
+   surjective … (Full_set ?) (Full_set ?) (canonical_proj ? (eqrel_of_morphism … f)).
  #A; #B; #f; nwhd; #y; #Hy; napply (ex_intro … y); napply conj
   [ napply I | napply refl]
 nqed.
 
 nlemma first_omomorphism_theorem_functions3:
- ∀A,B.∀f: unary_morphism A B. injective ?? (Full_set ?) (quotiented_mor ?? f).
+ ∀A,B.∀f: unary_morphism A B. 
+   injective … (Full_set ?) (quotiented_mor … f).
  #A; #B; #f; nwhd; #x; #x'; #Hx; #Hx'; #K; nassumption.
 nqed.
 
 nrecord isomorphism (A) (B) (S: qpowerclass A) (T: qpowerclass B) : CProp[0] ≝
  { iso_f:> unary_morphism A B;
    f_closed: ∀x. x ∈ S → iso_f x ∈ T;
-   f_sur: surjective ?? S T iso_f;
-   f_inj: injective ?? S iso_f
+   f_sur: surjective … S T iso_f;
+   f_inj: injective … S iso_f
  }.
diff --git a/helm/software/matita/nlibrary/topology/igft.ma b/helm/software/matita/nlibrary/topology/igft.ma
index 6628e36ef..b7818372b 100644
--- a/helm/software/matita/nlibrary/topology/igft.ma
+++ b/helm/software/matita/nlibrary/topology/igft.ma
@@ -1,4 +1,4 @@
-include "logic/connectives.ma".
+include "sets/sets.ma".
 
 nrecord powerset (X : Type[0]) : Type[1] ≝ { char : X → CProp[0] }.
 
-- 
2.39.2