1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "formal_topology/concrete_spaces.ma".
16 include "formal_topology/o-concrete_spaces.ma".
17 include "formal_topology/basic_pairs_to_o-basic_pairs.ma".
20 (* Qui, per fare le cose per bene, ci serve la nozione di funtore categorico *)
21 definition o_concrete_space_of_concrete_space: cic:/matita/formal_topology/concrete_spaces/concrete_space.ind#xpointer(1/1) → concrete_space.
24 [ apply (o_basic_pair_of_basic_pair (bp c));
25 | lapply depth=0 (downarrow c);
29 apply (o_operator_of_operator);fintersectsS);
38 definition o_convergent_relation_pair_of_convergent_relation_pair:
39 ∀BP1,BP2.cic:/matita/formal_topology/concrete_spaces/convergent_relation_pair.ind#xpointer(1/1) BP1 BP2 →
40 convergent_relation_pair (o_concrete_space_of_concrete_space BP1) (o_concrete_space_of_concrete_space BP2).
43 [ apply (orelation_of_relation ?? (r \sub \c));
44 | apply (orelation_of_relation ?? (r \sub \f));
45 | lapply (commute ?? r);
46 lapply (orelation_of_relation_preserves_equality ???? Hletin);
47 apply (.= (orelation_of_relation_preserves_composition (concr BP1) ??? (rel BP2)) ^ -1);
48 apply (.= (orelation_of_relation_preserves_equality ???? (commute ?? r)));
49 apply (orelation_of_relation_preserves_composition ?? (form BP2) (rel BP1) ?); ]