ogroups almost finished

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

diff --git a/matita/dama/excedence.ma b/matita/dama/excedence.ma
index d91c61170f10862ec14abf62f38ccb26f51e54b4..59b8baa4ed1668cae080c58dcaec9cb1fcc99f39 100644 (file)
--- a/matita/dama/excedence.ma
+++ b/matita/dama/excedence.ma
@@ -104,8 +104,7 @@ lemma lt_coreflexive: ∀E.coreflexive ? (lt E).
 intros 2 (E x); intro H; cases H (_ ABS); 
 apply (ap_coreflexive ? x ABS);
 qed.
-
-(* 
+ 
 lemma lt_transitive: ∀E.transitive ? (lt E).
 intros (E); unfold; intros (x y z H1 H2); cases H1 (Lxy Axy); cases H2 (Lyz Ayz); 
 split; [apply (le_transitive ???? Lxy Lyz)] clear H1 H2;
@@ -121,4 +120,20 @@ intros (E a b Lab); cases Lab (LEab Aab);
 cases Aab (H H); [cases (LEab H)] fold normalize (b ≰ a); assumption; (* BUG *)  
 qed.
 
-*)
\ No newline at end of file
+theorem le_le_to_eq: ∀E:excedence.∀x,y:E. x ≤ y → y ≤ x → x ≈ y.
+intros 6 (E x y L1 L2 H); cases H; [apply (L1 H1)|apply (L2 H1)]
+qed.
+
+lemma unfold_apart: ∀E:excedence. ∀x,y:E. x ≰ y ∨ y ≰ x → x # y.
+unfold apart_of_excedence; unfold apart; simplify; intros; assumption;
+qed.
+
+lemma le_rewl: ∀E:excedence.∀z,y,x:E. x ≈ y → x ≤ z → y ≤ z.
+intros (E z y x Exy Lxz); apply (le_transitive ???? ? Lxz);
+intro Xyz; apply Exy; apply unfold_apart; right; assumption;
+qed.
+
+lemma le_rewr: ∀E:excedence.∀z,y,x:E. x ≈ y → z ≤ x → z ≤ y.
+intros (E z y x Exy Lxz); apply (le_transitive ???? Lxz);
+intro Xyz; apply Exy; apply unfold_apart; left; assumption;
+qed.