More work on concrete spaces.

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces_to_o-concrete_spaces.ma b/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces_to_o-concrete_spaces.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 "concrete_spaces.ma".
+include "o-concrete_spaces.ma".
+include "basic_pairs_to_o-basic_pairs.ma".
+
+(* Qui, per fare le cose per bene, ci serve la nozione di funtore categorico *)
+definition o_concrete_space_of_concrete_space: cic:/matita/formal_topology/concrete_spaces/concrete_space.ind#xpointer(1/1) → concrete_space.
+ intro;
+ constructor 1;
+  [ apply (o_basic_pair_of_basic_pair (bp c));
+  | lapply depth=0 (downarrow c);
+    constructor 1;
+     [ apply 
+     |
+    apply (o_operator_of_operator);fintersectsS);
+  |
+  |
+  |
+  |
+  |
+  ]
+qed.
+
+definition o_convergent_relation_pair_of_convergent_relation_pair:
+ ∀BP1,BP2.cic:/matita/formal_topology/concrete_spaces/convergent_relation_pair.ind#xpointer(1/1) BP1 BP2 →
+  convergent_relation_pair (o_concrete_space_of_concrete_space BP1) (o_concrete_space_of_concrete_space BP2).
+ intros;
+ constructor 1;
+  [ apply (orelation_of_relation ?? (r \sub \c));
+  | apply (orelation_of_relation ?? (r \sub \f));
+  | lapply (commute ?? r);
+    lapply (orelation_of_relation_preserves_equality ???? Hletin);
+    apply (.= (orelation_of_relation_preserves_composition (concr BP1) ??? (rel BP2)) ^ -1);
+    apply (.= (orelation_of_relation_preserves_equality ???? (commute ?? r)));
+    apply (orelation_of_relation_preserves_composition ?? (form BP2)  (rel BP1) ?); ]
+qed.