better names

[helm.git] / helm / software / matita / contribs / dama / dama / models / nat_ordered_uniform.ma

diff --git a/helm/software/matita/contribs/dama/dama/models/nat_ordered_uniform.ma b/helm/software/matita/contribs/dama/dama/models/nat_ordered_uniform.ma
index 82eedb35a39bb883e8682793b0b814614da1c41d..becbab2fbb8125be50babfe7aab04f706f71d836 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/models/nat_ordered_uniform.ma
+++ b/helm/software/matita/contribs/dama/dama/models/nat_ordered_uniform.ma
@@ -18,11 +18,15 @@ include "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 7; cases H3; 
-cases H (_); cases (H8 y); apply H9; cases (H8 p);
-lapply (H12 H1) as H13; apply (le_le_eq);
-[1: apply (le_transitive ??? H4); apply (Le≪ ? H13); assumption;
-|2: apply (le_transitive ???? H5); apply (Le≫ ? (eq_sym ??? H13)); assumption;]
+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.