Stuff moved from old Matita.

[helm.git] / matita / matita / library / dama / models / nat_ordered_uniform.ma

diff --git a/matita/matita/library/dama/models/nat_ordered_uniform.ma b/matita/matita/library/dama/models/nat_ordered_uniform.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 "dama/models/nat_uniform.ma".  
+include "dama/bishop_set_rewrite.ma".
+include "dama/ordered_uniform.ma".
+
+definition nat_ordered_uniform_space:ordered_uniform_space.
+ apply (mk_ordered_uniform_space (mk_ordered_uniform_space_ ℕ ℕ (refl_eq ? ℕ)));
+simplify; intros 10;  cases H (_); cases (H7 y); apply H8; cases (H7 s);
+lapply (H11 H1) as H13; apply (le_le_eq);
+[2: apply (le_transitive ??? H5); apply (Le≪ ? H13); assumption;
+|1: assumption;
+|3: change with (le (os_r ℕ) (\snd y) (\fst y));
+    apply (ge_transitive ??? H5);apply (ge_transitive ???? H4);
+    change with (le (os_l ℕ) (\fst s) (\snd s));
+    apply (Le≫ ? H13); apply le_reflexive;
+|4: assumption;]
+qed. 
+ 
+interpretation "Ordered uniform space N" 'N = nat_ordered_uniform_space.