snapshot

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

diff --git a/matita/dama/ordered_groups.ma b/matita/dama/ordered_groups.ma
index c9cab27f85e542b71265fd2244dfa9c9a1ecdce8..9e72cab5944b57d3ab0d45cd947aa936efb17e9c 100644 (file)
--- a/matita/dama/ordered_groups.ma
+++ b/matita/dama/ordered_groups.ma
@@ -14,42 +14,23 @@
 
 set "baseuri" "cic:/matita/ordered_groups/".
 
-include "groups.ma".
 include "ordered_sets.ma".
+include "groups.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.
@@ -60,6 +41,19 @@ record ordered_abelian_group : Type ≝
     is_ordered_abelian_group og_pre_ordered_abelian_group
  }.
 
+lemma le_rewl: ∀E:excedence.∀x,z,y:E. x ≈ y → x ≤ z → y ≤ z.
+intros (E x z y); apply (le_transitive ???? ? H1); 
+clear H1 z; unfold in H; unfold; intro H1; apply H; clear H; 
+lapply ap_cotransitive;  
+intros (G x z y); intro Eyz; 
+
+
+lemma plus_cancr_le: 
+  ∀G:ordered_abelian_group.∀x,y,z:G.x+z ≤ y + z → x ≤ y.
+intros 5 (G x y z L);
+
+ apply L; clear L; elim (exc_cotransitive ???z Exy);
+
 lemma le_zero_x_to_le_opp_x_zero: 
   ∀G:ordered_abelian_group.∀x:G.0 ≤ x → -x ≤ 0.
 intros (G x Px);