X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fsoftware%2Fmatita%2Fdama%2Fordered_groups.ma;h=4d2e18e2838b081990d19dab8e8c573137036e93;hb=475120bb8ccfe5877bbe294006170ed7ab0b1fcd;hp=c9ef72c8ae4989ed600205ea88cf9dd29b5b6fe9;hpb=3a68c1b1f891a19d87c9963a5da2e4b76aadf455;p=helm.git

diff --git a/helm/software/matita/dama/ordered_groups.ma b/helm/software/matita/dama/ordered_groups.ma
index c9ef72c8a..4d2e18e28 100644
--- a/helm/software/matita/dama/ordered_groups.ma
+++ b/helm/software/matita/dama/ordered_groups.ma
@@ -18,38 +18,19 @@ include "groups.ma".
 include "ordered_sets.ma".
 
 record pre_ordered_abelian_group : Type ≝
- { og_abelian_group:> abelian_group;
-   og_tordered_set_: tordered_set;
-   og_with: exc_carr og_tordered_set_ = og_abelian_group
+ { og_abelian_group_: abelian_group;
+   og_tordered_set:> tordered_set;
+   og_with: carr og_abelian_group_ = og_tordered_set
  }.
 
-lemma og_tordered_set: pre_ordered_abelian_group → tordered_set.
-intro G; apply mk_tordered_set;
-[1: apply mk_pordered_set;
-    [1: apply (mk_excedence G); 
-        [1: cases G; clear G; simplify; rewrite < H; clear H;
-            cases og_tordered_set_; clear og_tordered_set_; simplify;
-            cases tos_poset; simplify; cases pos_carr; simplify; assumption;
-        |2: cases G; simplify; cases H; simplify; clear H; 
-            cases og_tordered_set_; simplify; clear og_tordered_set_;
-            cases tos_poset; simplify; cases pos_carr; simplify;
-            intros; apply H;
-        |3: cases G; simplify; cases H; simplify; cases og_tordered_set_; simplify;
-            cases tos_poset; simplify; cases pos_carr; simplify; 
-            intros; apply c; assumption]
-    |2: cases G; simplify;
-        cases H; simplify; clear H; cases og_tordered_set_; simplify;
-        cases tos_poset; simplify; assumption;]
-|2: simplify; (* SLOW, senza la simplify il widget muore *)
-    cases G; simplify; 
-    generalize in match (tos_totality og_tordered_set_);
-    unfold total_order_property;
-    cases H; simplify;  cases og_tordered_set_; simplify;
-    cases tos_poset; simplify; cases pos_carr; simplify;
-    intros; apply f; assumption;]
+lemma og_abelian_group: pre_ordered_abelian_group → abelian_group.
+intro G; apply (mk_abelian_group G); [1,2,3: rewrite < (og_with G)]
+[apply (plus (og_abelian_group_ G));|apply zero;|apply opp]
+unfold apartness_OF_pre_ordered_abelian_group; cases (og_with G); simplify;
+[apply plus_assoc|apply plus_comm|apply zero_neutral|apply opp_inverse|apply plus_strong_ext]
 qed.
 
-coercion cic:/matita/ordered_groups/og_tordered_set.con.
+coercion cic:/matita/ordered_groups/og_abelian_group.con.
 
 definition is_ordered_abelian_group ≝
  λG:pre_ordered_abelian_group. ∀f,g,h:G. f≤g → f+h≤g+h.
@@ -65,9 +46,9 @@ lemma le_zero_x_to_le_opp_x_zero:
 intros (G x Px);
 generalize in match (og_ordered_abelian_group_properties ? ? ? (-x) Px); intro;
 (* ma cazzo, qui bisogna rifare anche i gruppi con ≈ ? *)
- rewrite > zero_neutral in H1;
- rewrite > plus_comm in H1;
- rewrite > opp_inverse in H1;
+ rewrite > zero_neutral in H;
+ rewrite > plus_comm in H;
+ rewrite > opp_inverse in H;
  assumption.
 qed.