helm/software/matita/dama/metric_lattice.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 set "baseuri" "cic:/matita/metric_lattice/".
  16
  17 include "metric_space.ma".
  18 include "lattice.ma".
  19
  20 record mlattice (R : ogroup) : Type ≝ {
  21   ml_mspace_: metric_space R;
  22   ml_lattice:> lattice;
  23   ml_with_: ms_carr ? ml_mspace_ = ap_carr (l_carr ml_lattice)
  24 }.
  25
  26 lemma ml_mspace: ∀R.mlattice R → metric_space R.
  27 intros (R ml); apply (mk_metric_space R ml); unfold Type_OF_mlattice;
  28 cases (ml_with_ ? ml); simplify;
  29 [apply (metric ? (ml_mspace_ ? ml));|apply (mpositive ? (ml_mspace_ ? ml));
  30 |apply (mreflexive ? (ml_mspace_ ? ml));|apply (msymmetric ? (ml_mspace_ ? ml));
  31 |apply (mtineq ? (ml_mspace_ ? ml))]
  32 qed.
  33
  34 coercion cic:/matita/metric_lattice/ml_mspace.con.