fixed bugs found by csc

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

diff --git a/matita/dama/excedence.ma b/matita/dama/excedence.ma
index 950639fed11a8e0c0cc6e7b6f3fc53981bd8fcbd..c2a5ffd4fde20049391060de83b85f2cd22cf310 100644 (file)
--- a/matita/dama/excedence.ma
+++ b/matita/dama/excedence.ma
@@ -21,7 +21,7 @@ include "constructive_higher_order_relations.ma".
 
 record excedence : Type ≝ {
   exc_carr:> Type;
-  exc_relation: exc_carr → exc_carr → Type; (* Big bug: era in Prop!!! *)
+  exc_relation: exc_carr → exc_carr → Type;
   exc_coreflexive: coreflexive ? exc_relation;
   exc_cotransitive: cotransitive ? exc_relation 
 }.
@@ -79,22 +79,22 @@ lemma eq_reflexive:∀E. reflexive ? (eq E).
 intros (E); unfold; intros (x); apply ap_coreflexive; 
 qed.
 
-lemma eq_symmetric:∀E.symmetric ? (eq E).
+lemma eq_sym_:∀E.symmetric ? (eq E).
 intros (E); unfold; intros (x y Exy); unfold; unfold; intros (Ayx); apply Exy;
 apply ap_symmetric; assumption; 
 qed.
 
-lemma eq_symmetric_:∀E:apartness.∀x,y:E.x ≈ y → y ≈ x := eq_symmetric.
+lemma eq_sym:∀E:apartness.∀x,y:E.x ≈ y → y ≈ x := eq_sym_.
 
-coercion cic:/matita/excedence/eq_symmetric_.con.
+coercion cic:/matita/excedence/eq_sym.con.
 
-lemma eq_transitive_: ∀E.transitive ? (eq E).
+lemma eq_trans_: ∀E.transitive ? (eq E).
 (* bug. intros k deve fare whd quanto basta *)
 intros 6 (E x y z Exy Eyz); intro Axy; cases (ap_cotransitive ???y Axy); 
 [apply Exy|apply Eyz] assumption.
 qed.
 
-lemma eq_transitive:∀E:apartness.∀x,y,z:E.x ≈ y → y ≈ z → x ≈ z ≝ eq_transitive_.
+lemma eq_trans:∀E:apartness.∀x,y,z:E.x ≈ y → y ≈ z → x ≈ z ≝ eq_trans_.
 
 (* BUG: vedere se ricapita *)
 lemma le_antisymmetric: ∀E.antisymmetric ? (le E) (eq ?).
@@ -127,12 +127,6 @@ intros (E a b Lab); cases Lab (LEab Aab);
 cases Aab (H H); [cases (LEab H)] fold normalize (b ≰ a); assumption; (* BUG *)  
 qed.
 
-(* CSC: lo avevi gia' dimostrato; ho messo apply! *)
-theorem le_le_to_eq: ∀E:excedence.∀x,y:E. x ≤ y → y ≤ x → x ≈ y.
-apply le_antisymmetric;
-qed.
-
-(* CSC: perche' quel casino: bastava intros; assumption! *)
 lemma unfold_apart: ∀E:excedence. ∀x,y:E. x ≰ y ∨ y ≰ x → x # y.
 intros; assumption;
 qed.
@@ -155,4 +149,14 @@ qed.
 lemma ap_rewr: ∀A:apartness.∀x,z,y:A. x ≈ y → z # y → z # x.
 intros (A x z y Exy Azy); apply ap_symmetric; apply (ap_rewl ???? Exy);
 apply ap_symmetric; assumption;
-qed.
\ No newline at end of file
+qed.
+
+lemma exc_rewl: ∀A:excedence.∀x,z,y:A. x ≈ y → y ≰ z → x ≰ z.
+intros (A x z y Exy Ayz); elim (exc_cotransitive ???x Ayz); [2:assumption]
+cases Exy; right; assumption;
+qed.
+  
+lemma exc_rewr: ∀A:excedence.∀x,z,y:A. x ≈ y → z ≰ y → z ≰ x.
+intros (A x z y Exy Azy); elim (exc_cotransitive ???x Azy); [assumption]
+elim (Exy); left; assumption;
+qed.