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[helm.git] / helm / software / matita / contribs / formal_topology / overlap / o-formal_topologies.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-formal_topologies.ma b/helm/software/matita/contribs/formal_topology/overlap/o-formal_topologies.ma
index 1693b55f61eb62677243c92d2e0a61380477adac..e750dcc900f62e67a2773af66796401d5570022a 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/o-formal_topologies.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-formal_topologies.ma
@@ -12,16 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "o-concrete_spaces.ma".
-
-definition btop_carr: BTop → Type ≝ λo:BTop. carr (carrbt o).
-
-coercion btop_carr.
-
-definition btop_carr': BTop → setoid ≝ λo:BTop. carrbt o.
-
-coercion btop_carr'.
+include "o-basic_topologies.ma".
 
+(*
 definition downarrow: ∀S:BTop. unary_morphism (Ω \sup S) (Ω \sup S).
  intros; constructor 1;
   [ apply (λU:Ω \sup S.{a | ∃b:carrbt S. b ∈ U ∧ a ∈ A ? (singleton ? b)});
@@ -40,15 +33,14 @@ definition ffintersects: ∀S:BTop. binary_morphism1 (Ω \sup S) (Ω \sup S) (Ω
 qed.
 
 interpretation "ffintersects" 'fintersects U V = (fun1 ___ (ffintersects _) U V).
+*)
 
 record formal_topology: Type ≝
  { bt:> BTop;
-   converges: ∀U,V: Ω \sup bt. A ? (U ↓ V) = A ? U ∩ A ? V
+   converges: ∀U,V: bt. A ? (U ↓ V) = (A ? U ∧ A ? V)
  }.
 
-definition bt': formal_topology → basic_topology ≝ λo:formal_topology.bt o.
-
-coercion bt'.
+(*
 
 definition ffintersects': ∀S:BTop. binary_morphism1 S S (Ω \sup S).
  intros; constructor 1;
@@ -57,18 +49,13 @@ definition ffintersects': ∀S:BTop. binary_morphism1 S S (Ω \sup S).
 qed.
 
 interpretation "ffintersects'" 'fintersects U V = (fun1 ___ (ffintersects' _) U V).
-
+*)
 record formal_map (S,T: formal_topology) : Type ≝
  { cr:> continuous_relation_setoid S T;
    C1: ∀b,c. extS ?? cr (b ↓ c) = ext ?? cr b ↓ ext ?? cr c;
    C2: extS ?? cr T = S
  }.
 
-definition cr': ∀FT1,FT2.formal_map FT1 FT2 → continuous_relation FT1 FT2 ≝
- λFT1,FT2,c. cr FT1 FT2 c.
-
-coercion cr'.
-
 definition formal_map_setoid: formal_topology → formal_topology → setoid1.
  intros (S T); constructor 1;
   [ apply (formal_map S T);
@@ -79,16 +66,6 @@ definition formal_map_setoid: formal_topology → formal_topology → setoid1.
      | simplify; intros 3; apply trans1]]
 qed.
 
-definition cr'': ∀FT1,FT2.formal_map_setoid FT1 FT2 → arrows1 BTop FT1 FT2 ≝
- λFT1,FT2,c.cr ?? c.
-
-coercion cr''.
-
-definition cr''': ∀FT1,FT2.formal_map_setoid FT1 FT2 → arrows1 REL FT1 FT2 ≝
- λFT1,FT2:formal_topology.λc:formal_map_setoid FT1 FT2.cont_rel FT1 FT2 (cr' ?? c).
-
-coercion cr'''.
-
 axiom C1':
  ∀S,T: formal_topology.∀f:formal_map_setoid S T.∀U,V: Ω \sup T.
   extS ?? f (U ↓ V) = extS ?? f U ↓ extS ?? f V.