minus in nat.ma

[helm.git] / helm / software / matita / library / nat / count.ma

diff --git a/helm/software/matita/library/nat/count.ma b/helm/software/matita/library/nat/count.ma
index 20913fa6041c103527cfd73e7a5c7708b15924de..73e251bf6b35929353622914eb364e393ad85a5f 100644 (file)
--- a/helm/software/matita/library/nat/count.ma
+++ b/helm/software/matita/library/nat/count.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/nat/count".
-
 include "nat/relevant_equations.ma".
 include "nat/sigma_and_pi.ma".
 include "nat/permutation.ma".
@@ -35,7 +33,7 @@ theorem sigma_plus: \forall n,p,m:nat.\forall f:nat \to nat.
 sigma (S (p+n)) f m = sigma p (\lambda x.(f ((S n) + x))) m + sigma n f m.
 intros. elim p.
 simplify.
-rewrite < (sym_plus n m).reflexivity.
+reflexivity.
 simplify.
 rewrite > assoc_plus in \vdash (? ? ? %).
 rewrite < H.
@@ -70,9 +68,7 @@ sigma m (\lambda a.(sigma n (\lambda b.f (b*(S m) + a)) O)) O.
 intro.elim n.simplify.
 rewrite < plus_n_O.
 apply eq_sigma.intros.reflexivity.
-change with 
-(sigma (m+(S n1)*(S m)) f O =
-sigma m (\lambda a.(f ((S(n1+O))*(S m)+a)) + (sigma n1 (\lambda b.f (b*(S m)+a)) O)) O).
+simplify.
 rewrite > sigma_f_g.
 rewrite < plus_n_O.
 rewrite < H.
@@ -158,8 +154,7 @@ apply (trans_eq ? ?
 (sigma m (\lambda n.(bool_to_nat (f2 n))*(bool_to_nat (f1 i))) O)).
 reflexivity.
 apply sym_eq. apply sigma_times.
-change in match (pred (S n)) with n.
-change in match (pred (S m)) with m.
+simplify.
 apply sym_eq. apply sigma_times.
 unfold permut.
 split.