moved formal_topology into library"

[helm.git] / helm / software / matita / contribs / formal_topology / overlap / basic_topologies_to_o-basic_topologies.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/basic_topologies_to_o-basic_topologies.ma b/helm/software/matita/contribs/formal_topology/overlap/basic_topologies_to_o-basic_topologies.ma
deleted file mode 100644 (file)
index bea3207..0000000
--- a/helm/software/matita/contribs/formal_topology/overlap/basic_topologies_to_o-basic_topologies.ma
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_topologies.ma".
-include "o-basic_topologies.ma".
-include "relations_to_o-algebra.ma".
-
-definition o_basic_topology_of_basic_topology: basic_topology → Obasic_topology.
- intros (b); constructor 1;
-  [ apply (POW' b) | apply (A b) | apply (J b);
-  | apply (A_is_saturation b) | apply (J_is_reduction b) | apply (compatibility b) ]
-qed.
-
-definition o_continuous_relation_of_continuous_relation:
- ∀BT1,BT2.continuous_relation BT1 BT2 →
-  Ocontinuous_relation (o_basic_topology_of_basic_topology BT1) (o_basic_topology_of_basic_topology BT2).
- intros (BT1 BT2 c); constructor 1;
-  [ apply (orelation_of_relation ?? c) | apply (reduced ?? c) | apply (saturated ?? c) ]
-qed.
-
-axiom daemon: False.
-
-lemma o_continuous_relation_of_continuous_relation_morphism :
-  ∀S,T:category2_of_category1 BTop.
-  unary_morphism2 (arrows2 (category2_of_category1 BTop) S T)
-   (arrows2 OBTop (o_basic_topology_of_basic_topology S) (o_basic_topology_of_basic_topology T)).
-intros (S T);
-   constructor 1;
-     [ apply (o_continuous_relation_of_continuous_relation S T);
-     | cases daemon (*apply (o_relation_pair_of_relation_pair_is_morphism S T)*)]
-qed.
-
-definition BTop_to_OBTop: carr3 (arrows3 CAT2 (category2_of_category1 BTop) OBTop).
- constructor 1;
-  [ apply o_basic_topology_of_basic_topology;
-  | intros; apply o_continuous_relation_of_continuous_relation_morphism;
-  | cases daemon (*apply o_relation_topology_of_relation_topology_morphism_respects_id*);
-  | cases daemon (*apply o_relation_topology_of_relation_topology_morphism_respects_comp*);]
-qed.
-
-(*
-alias symbol "eq" (instance 2) = "setoid1 eq".
-alias symbol "eq" (instance 1) = "setoid2 eq".
-theorem BTop_to_OBTop_faithful:
- ∀S,T.∀f,g:arrows2 (category2_of_category1 BTop) S T.
-  map_arrows2 ?? BTop_to_OBTop ?? f = map_arrows2 ?? BTop_to_OBTop ?? g → f=g.
- intros; change with (∀b.A ? (ext ?? f b) = A ? (ext ?? g b));
- apply (POW_faithful);
- apply (.= respects_comp2 ?? POW (concr S) (concr T) (form T) f \sub \c (⊩ \sub T));
- apply sym2;
- apply (.= respects_comp2 ?? POW (concr S) (concr T) (form T) g \sub \c (⊩ \sub T));
- apply sym2;
- apply e;
-qed.
-*)
-
-include "notation.ma".
-
-theorem BTop_to_OBTop_full: 
-   ∀S,T.∀f. exT22 ? (λg. map_arrows2 ?? BTop_to_OBTop S T g = f).
- intros;
- cases (POW_full (carrbt S) (carrbt T) (Ocont_rel ?? f)) (g Hg);
- exists[
-   constructor 1;
-    [ apply g
-    | apply hide; intros; lapply (Oreduced ?? f ? e);
-      cases Hg; lapply (e3 U) as K; apply (.= K);
-      apply (.= Hletin); apply rule (†(K^-1));
-    | apply hide; intros; lapply (Osaturated ?? f ? e);
-      cases Hg; lapply (e1 U) as K; apply (.= K);
-      apply (.= Hletin); apply rule (†(K^-1));
-    ]
- | simplify; unfold BTop_to_OBTop; simplify;
-   unfold o_continuous_relation_of_continuous_relation_morphism; simplify;
-   cases Hg; whd; simplify; intro; 
-qed.
\ No newline at end of file