From 6302e8ebc63beb73aa672c9c23199bdfaa3f8715 Mon Sep 17 00:00:00 2001 From: Claudio Sacerdoti Coen Date: Tue, 6 Jan 2009 17:44:05 +0000 Subject: [PATCH] More work on concrete spaces. --- .../overlap/concrete_spaces.ma | 2 +- .../concrete_spaces_to_o-concrete_spaces.ma | 49 +++++++++++++++++++ .../contribs/formal_topology/overlap/depends | 1 + 3 files changed, 51 insertions(+), 1 deletion(-) create mode 100644 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.ma b/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces.ma index ff6774be3..5ce337c6f 100644 --- a/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces.ma +++ b/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces.ma @@ -27,7 +27,7 @@ coercion bp'. definition bp'': concrete_space → objs1 BP ≝ λc.bp c. coercion bp''. -record convergent_relation_pair (CS1,CS2: concrete_space) : Type ≝ +record convergent_relation_pair (CS1,CS2: concrete_space) : Type1 ≝ { rp:> arrows1 ? CS1 CS2; respects_converges: ∀b,c. 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 new file mode 100644 index 000000000..40670ba72 --- /dev/null +++ b/helm/software/matita/contribs/formal_topology/overlap/concrete_spaces_to_o-concrete_spaces.ma @@ -0,0 +1,49 @@ +(**************************************************************************) +(* ___ *) +(* ||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. diff --git a/helm/software/matita/contribs/formal_topology/overlap/depends b/helm/software/matita/contribs/formal_topology/overlap/depends index 50152aeab..ef49925f3 100644 --- a/helm/software/matita/contribs/formal_topology/overlap/depends +++ b/helm/software/matita/contribs/formal_topology/overlap/depends @@ -12,6 +12,7 @@ subsets.ma categories.ma basic_topologies.ma relations.ma saturations.ma concrete_spaces.ma basic_pairs.ma relations.ma subsets.ma +concrete_spaces_to_o-concrete_spaces.ma basic_pairs_to_o-basic_pairs.ma concrete_spaces.ma o-concrete_spaces.ma o-basic_topologies.ma o-algebra.ma o-saturations.ma basic_pairs_to_o-basic_pairs.ma basic_pairs.ma o-basic_pairs.ma relations_to_o-algebra.ma basic_topologies_to_o-basic_topologies.ma basic_topologies.ma o-basic_topologies.ma relations_to_o-algebra.ma -- 2.39.2