moved formal_topology into library"

[helm.git] / helm / software / matita / contribs / formal_topology / overlap / concrete_spaces.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces.ma b/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces.ma
deleted file mode 100644 (file)
index 791af46..0000000
--- a/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces.ma
+++ /dev/null
@@ -1,109 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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_pairs.ma".
-
-(* carr1 e' necessario perche' ci sega via la coercion per gli oggetti di REL!
-   (confondendola con la coercion per gli oggetti di SET *)
-record concrete_space : Type1 ≝
- { bp:> BP;
-   converges: ∀a: carr1 (concr bp).∀U,V: carr1 (form bp). a ⊩ U → a ⊩ V → a ⊩ (U ↓ V);
-   all_covered: ∀x: carr1 (concr bp). x ⊩ form bp
- }.
-
-record convergent_relation_pair (CS1,CS2: concrete_space) : Type1 ≝
- { rp:> arrows1 ? CS1 CS2;
-   respects_converges:
-    ∀b,c.
-     minus_image ?? rp \sub\c (BPextS CS2 (b ↓ c)) =
-     BPextS CS1 ((minus_image ?? rp \sub\f b) ↓ (minus_image ?? rp \sub\f c));
-   respects_all_covered:
-    minus_image ?? rp\sub\c (BPextS CS2 (full_subset (form CS2))) = BPextS CS1 (full_subset (form CS1))
- }.
-(*
-definition convergent_relation_space_setoid: concrete_space → concrete_space → setoid1.
- intros;
- constructor 1;
-  [ apply (convergent_relation_pair c c1)
-  | constructor 1;
-     [ intros;
-       apply (relation_pair_equality c c1 c2 c3);
-     | intros 1; apply refl1;
-     | intros 2; apply sym1; 
-     | intros 3; apply trans1]]
-qed.
-
-definition convergent_relation_space_composition:
- ∀o1,o2,o3: concrete_space.
-  binary_morphism1
-   (convergent_relation_space_setoid o1 o2)
-   (convergent_relation_space_setoid o2 o3)
-   (convergent_relation_space_setoid o1 o3).
- intros; constructor 1;
-     [ intros; whd in c c1 ⊢ %;
-       constructor 1;
-        [ apply (fun1 ??? (comp1 BP ???)); [apply (bp o2) |*: apply rp; assumption]
-        | intros;
-          change in ⊢ (? ? ? (? ? ? (? ? ? %) ?) ?) with (c1 \sub \c ∘ c \sub \c);
-          change in ⊢ (? ? ? ? (? ? ? ? (? ? ? ? ? (? ? ? (? ? ? %) ?) ?)))
-            with (c1 \sub \f ∘ c \sub \f);
-          change in ⊢ (? ? ? ? (? ? ? ? (? ? ? ? ? ? (? ? ? (? ? ? %) ?))))
-            with (c1 \sub \f ∘ c \sub \f);
-          apply (.= (extS_com ??????));
-          apply (.= (†(respects_converges ?????)));
-          apply (.= (respects_converges ?????));
-          apply (.= (†(((extS_com ??????) \sup -1)‡(extS_com ??????)\sup -1)));
-          apply refl1;
-        | change in ⊢ (? ? ? (? ? ? (? ? ? %) ?) ?) with (c1 \sub \c ∘ c \sub \c);
-          apply (.= (extS_com ??????));
-          apply (.= (†(respects_all_covered ???)));
-          apply (.= respects_all_covered ???);
-          apply refl1]
-     | intros;
-       change with (b ∘ a = b' ∘ a');
-       change in H with (rp'' ?? a = rp'' ?? a');
-       change in H1 with (rp'' ?? b = rp ?? b');
-       apply (.= (H‡H1));
-       apply refl1]
-qed.
-
-definition CSPA: category1.
- constructor 1;
-  [ apply concrete_space
-  | apply convergent_relation_space_setoid
-  | intro; constructor 1;
-     [ apply id1
-     | intros;
-       unfold id; simplify;
-       apply (.= (equalset_extS_id_X_X ??));
-       apply (.= (†((equalset_extS_id_X_X ??)\sup -1‡
-                    (equalset_extS_id_X_X ??)\sup -1)));
-       apply refl1;
-     | apply (.= (equalset_extS_id_X_X ??));
-       apply refl1]
-  | apply convergent_relation_space_composition
-  | intros; simplify;
-    change with (a34 ∘ (a23 ∘ a12) = (a34 ∘ a23) ∘ a12);
-    apply (.= ASSOC1);
-    apply refl1
-  | intros; simplify;
-    change with (a ∘ id1 ? o1 = a);
-    apply (.= id_neutral_right1 ????);
-    apply refl1
-  | intros; simplify;
-    change with (id1 ? o2 ∘ a = a);
-    apply (.= id_neutral_left1 ????);
-    apply refl1]
-qed.
-*)
\ No newline at end of file