some work till the need of redoing all groups based on excedence

[helm.git] / matita / dama / ordered_groups.ma

diff --git a/matita/dama/ordered_groups.ma b/matita/dama/ordered_groups.ma
index 10e8f189ab0d4aeea549902fa4c2671372188f48..c9ef72c8ae4989ed600205ea88cf9dd29b5b6fe9 100644 (file)
--- a/matita/dama/ordered_groups.ma
+++ b/matita/dama/ordered_groups.ma
@@ -19,29 +19,37 @@ include "ordered_sets.ma".
 
 record pre_ordered_abelian_group : Type ≝
  { og_abelian_group:> abelian_group;
-   og_ordered_set_: ordered_set;
-   og_with: os_carrier og_ordered_set_ = og_abelian_group
+   og_tordered_set_: tordered_set;
+   og_with: exc_carr og_tordered_set_ = og_abelian_group
  }.
 
-lemma og_ordered_set: pre_ordered_abelian_group → ordered_set.
- intro G;
- apply mk_ordered_set;
-  [ apply (carrier (og_abelian_group G))
-  | apply (eq_rect ? ? (λC:Type.C→C→Prop) ? ? (og_with G));
-    apply os_le
-  | apply
-     (eq_rect' ? ?
-       (λa:Type.λH:os_carrier (og_ordered_set_ G) = a.
-        is_order_relation a
-         (eq_rect Type (og_ordered_set_ G) (λC:Type.C→C→Prop)
-          (os_le (og_ordered_set_ G)) a H))
-       ? ? (og_with G));
-    simplify;
-    apply (os_order_relation_properties (og_ordered_set_ G))
-  ]
+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;]
 qed.
 
-coercion cic:/matita/ordered_groups/og_ordered_set.con.
+coercion cic:/matita/ordered_groups/og_tordered_set.con.
 
 definition is_ordered_abelian_group ≝
  λG:pre_ordered_abelian_group. ∀f,g,h:G. f≤g → f+h≤g+h.
@@ -52,9 +60,11 @@ record ordered_abelian_group : Type ≝
     is_ordered_abelian_group og_pre_ordered_abelian_group
  }.
 
-lemma le_zero_x_to_le_opp_x_zero: ∀G:ordered_abelian_group.∀x:G.0 ≤ x → -x ≤ 0.
- intros;
- generalize in match (og_ordered_abelian_group_properties ? ? ? (-x) H); intro;
+lemma le_zero_x_to_le_opp_x_zero: 
+  ∀G:ordered_abelian_group.∀x:G.0 ≤ x → -x ≤ 0.
+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;