X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fdama%2Fgroup.ma;h=104dcf274e3943727d090dc8ff8fddd5f7bca59e;hb=9483f7e6c85ec11f88bdb219b2cebad2039b1a74;hp=0e2668c2d71c58923390538a8753fff9868158df;hpb=87ed0c3e2ccd74f21f81c2cc9ed2945109bf0a9a;p=helm.git

diff --git a/helm/software/matita/dama/group.ma b/helm/software/matita/dama/group.ma
index 0e2668c2d..104dcf274 100644
--- a/helm/software/matita/dama/group.ma
+++ b/helm/software/matita/dama/group.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/group/".
+
 
 include "excess.ma".
 
@@ -80,7 +80,7 @@ coercion cic:/matita/group/feq_plusl.con nocomposites.
 lemma plus_strong_extr: ∀G:abelian_group.∀z:G.strong_ext ? (λx.x + z).
 intros 5 (G z x y A); simplify in A;
 lapply (plus_comm ? z x) as E1; lapply (plus_comm ? z y) as E2;
-lapply (ap_rewl ???? E1 A) as A1; lapply (ap_rewr ???? E2 A1) as A2;
+lapply (Ap≪ ? E1 A) as A1; lapply (Ap≫ ? E2 A1) as A2;
 apply (plus_strong_ext ???? A2);
 qed.
 
@@ -111,31 +111,31 @@ coercion cic:/matita/group/feq_plusl_sym_.con nocomposites.
       
 lemma fap_plusl: ∀G:abelian_group.∀x,y,z:G. y # z →  x+y # x+z. 
 intros (G x y z Ayz); apply (plus_strong_ext ? (-x));
-apply (ap_rewl ??? ((-x + x) + y));
+apply (Ap≪ ((-x + x) + y));
 [1: apply plus_assoc; 
-|2: apply (ap_rewr ??? ((-x +x) +z));
+|2: apply (Ap≫ ((-x +x) +z));
     [1: apply plus_assoc; 
-    |2: apply (ap_rewl ??? (0 + y));
+    |2: apply (Ap≪ (0 + y));
         [1: apply (feq_plusr ???? (opp_inverse ??)); 
-        |2: apply (ap_rewl ???? (zero_neutral ? y)); 
-            apply (ap_rewr ??? (0 + z) (opp_inverse ??)); 
-            apply (ap_rewr ???? (zero_neutral ??)); assumption;]]]
+        |2: apply (Ap≪ ? (zero_neutral ? y)); 
+            apply (Ap≫ (0 + z) (opp_inverse ??)); 
+            apply (Ap≫ ? (zero_neutral ??)); assumption;]]]
 qed.
 
 lemma fap_plusr: ∀G:abelian_group.∀x,y,z:G. y # z →  y+x # z+x. 
 intros (G x y z Ayz); apply (plus_strong_extr ? (-x));
-apply (ap_rewl ??? (y + (x + -x)));
+apply (Ap≪ (y + (x + -x)));
 [1: apply (eq_sym ??? (plus_assoc ????)); 
-|2: apply (ap_rewr ??? (z + (x + -x)));
+|2: apply (Ap≫ (z + (x + -x)));
     [1: apply (eq_sym ??? (plus_assoc ????)); 
-    |2: apply (ap_rewl ??? (y + (-x+x)) (plus_comm ? x (-x)));
-        apply (ap_rewl ??? (y + 0) (opp_inverse ??));
-        apply (ap_rewl ??? (0 + y) (plus_comm ???));
-        apply (ap_rewl ??? y (zero_neutral ??));
-        apply (ap_rewr ??? (z + (-x+x)) (plus_comm ? x (-x)));
-        apply (ap_rewr ??? (z + 0) (opp_inverse ??));
-        apply (ap_rewr ??? (0 + z) (plus_comm ???));
-        apply (ap_rewr ??? z (zero_neutral ??));
+    |2: apply (Ap≪ (y + (-x+x)) (plus_comm ? x (-x)));
+        apply (Ap≪ (y + 0) (opp_inverse ??));
+        apply (Ap≪ (0 + y) (plus_comm ???));
+        apply (Ap≪ y (zero_neutral ??));
+        apply (Ap≫ (z + (-x+x)) (plus_comm ? x (-x)));
+        apply (Ap≫ (z + 0) (opp_inverse ??));
+        apply (Ap≫ (0 + z) (plus_comm ???));
+        apply (Ap≫ z (zero_neutral ??));
         assumption]]
 qed.
 
@@ -183,7 +183,6 @@ qed.
 
 lemma feq_oppr: ∀G:abelian_group.∀x,y,z:G. y ≈ z → x ≈ -y → x ≈ -z.
 intros (G x y z H1 H2); apply (plus_cancr ??? z);
-(* apply (eq_trans ??? 0 ? (opp_inverse ??)); *)
 apply (Eq≈ 0 ? (opp_inverse ??));
 apply (Eq≈ (-y + z) H2);
 apply (Eq≈ (-y + y) H1);