X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Ftimes.ma;h=f59622218e84c38535f862a7f8917fd7a5b4d87d;hb=e880d6eab5e1700f4a625ddcd7d0fa8f0cce2dcc;hp=ec0f861998c2314536888bae8882de035fb21682;hpb=3f5a0152427fd9a89e7239befd259d27b97aaef5;p=helm.git

diff --git a/helm/software/matita/library/nat/times.ma b/helm/software/matita/library/nat/times.ma
index ec0f86199..f59622218 100644
--- a/helm/software/matita/library/nat/times.ma
+++ b/helm/software/matita/library/nat/times.ma
@@ -1,3 +1,4 @@
+
 (**************************************************************************)
 (*       __                                                               *)
 (*      ||M||                                                             *)
@@ -12,8 +13,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/nat/times".
-
 include "nat/plus.ma".
 
 let rec times n m \def 
@@ -21,7 +20,12 @@ let rec times n m \def
  [ O \Rightarrow O
  | (S p) \Rightarrow m+(times p m) ].
 
-interpretation "natural times" 'times x y = (cic:/matita/nat/times/times.con x y).
+interpretation "natural times" 'times x y = (times x y).
+
+theorem times_Sn_m:
+\forall n,m:nat. m+n*m = S n*m.
+intros. reflexivity.
+qed.
 
 theorem times_n_O: \forall n:nat. O = n*O.
 intros.elim n.
@@ -33,13 +37,17 @@ theorem times_n_Sm :
 \forall n,m:nat. n+(n*m) = n*(S m).
 intros.elim n.
 simplify.reflexivity.
-simplify.apply eq_f.rewrite < H.
+simplify.
+demodulate all.
+(*
+apply eq_f.rewrite < H.
 transitivity ((n1+m)+n1*m).symmetry.apply assoc_plus.
 transitivity ((m+n1)+n1*m).
 apply eq_f2.
 apply sym_plus.
 reflexivity.
 apply assoc_plus.
+*)
 qed.
 
 theorem times_O_to_O: \forall n,m:nat.n*m = O \to n = O \lor m= O.
@@ -53,11 +61,11 @@ apply nat_elim2;intros
 qed.
 
 theorem times_n_SO : \forall n:nat. n = n * S O.
-intros.
+intros. demodulate. reflexivity. (*
 rewrite < times_n_Sm.
 rewrite < times_n_O.
 rewrite < plus_n_O.
-reflexivity.
+reflexivity.*)
 qed.
 
 theorem times_SSO_n : \forall n:nat. n + n = S (S O) * n.
@@ -90,9 +98,11 @@ qed.
 
 theorem symmetric_times : symmetric nat times. 
 unfold symmetric.
-intros.elim x.
-simplify.apply times_n_O.
-simplify.rewrite > H.apply times_n_Sm.
+intros.elim x;
+ [ simplify. apply times_n_O.
+ | demodulate. reflexivity. (*
+(* applyS times_n_Sm. *) 
+simplify.rewrite > H.apply times_n_Sm.*)]
 qed.
 
 variant sym_times : \forall n,m:nat. n*m = m*n \def
@@ -102,23 +112,38 @@ theorem distributive_times_plus : distributive nat times plus.
 unfold distributive.
 intros.elim x.
 simplify.reflexivity.
-simplify.rewrite > H. rewrite > assoc_plus.rewrite > assoc_plus.
+simplify.
+demodulate all.
+(*
+rewrite > H. rewrite > assoc_plus.rewrite > assoc_plus.
 apply eq_f.rewrite < assoc_plus. rewrite < (sym_plus ? z).
-rewrite > assoc_plus.reflexivity.
+rewrite > assoc_plus.reflexivity. *)
 qed.
 
 variant distr_times_plus: \forall n,m,p:nat. n*(m+p) = n*m + n*p
 \def distributive_times_plus.
 
 theorem associative_times: associative nat times.
-unfold associative.intros.
-elim x.simplify.apply refl_eq.
-simplify.rewrite < sym_times.
+unfold associative.
+intros.
+elim x. simplify.apply refl_eq. 
+simplify.
+demodulate all.
+(*
+rewrite < sym_times.
 rewrite > distr_times_plus.
 rewrite < sym_times.
 rewrite < (sym_times (times n y) z).
 rewrite < H.apply refl_eq.
+*)
 qed.
 
 variant assoc_times: \forall n,m,p:nat. (n*m)*p = n*(m*p) \def
 associative_times.
+
+lemma times_times: ∀x,y,z. x*(y*z) = y*(x*z).
+intros. 
+demodulate. reflexivity.
+(* autobatch paramodulation. *)
+qed.
+