* Obsolete debugging comments removed

[helm.git] / helm / matita / library / nat / div_and_mod.ma

diff --git a/helm/matita/library/nat/div_and_mod.ma b/helm/matita/library/nat/div_and_mod.ma
index e4645c3071a78903a14039be49d0ff504e7c62e7..73344c7c46b0cf1466b0aea949755ced792fc13a 100644 (file)
--- a/helm/matita/library/nat/div_and_mod.ma
+++ b/helm/matita/library/nat/div_and_mod.ma
@@ -15,8 +15,6 @@
 set "baseuri" "cic:/matita/nat/div_and_mod".
 
 include "nat/minus.ma".
-include "nat/le_arith.ma".
-include "nat/compare.ma".
 
 let rec mod_aux p m n: nat \def
 match (leb m n) with
@@ -128,15 +126,14 @@ cut b \leq (q1-q)*b+r1.
 cut b \leq r.
 apply lt_to_not_le r b H2 Hcut2.
 elim Hcut.assumption.
-apply trans_le ? ((q1-q)*b) ?.
+apply trans_le ? ((q1-q)*b).
 apply le_times_n.
 apply le_SO_minus.exact H6.
 rewrite < sym_plus.
 apply le_plus_n.
 rewrite < sym_times.
 rewrite > distr_times_minus.
-(* ATTENZIONE ALL' ORDINAMENTO DEI GOALS *)
-rewrite > plus_minus ? ? ? ?.
+rewrite > plus_minus.
 rewrite > sym_times.
 rewrite < H5.
 rewrite < sym_times.
@@ -156,14 +153,14 @@ cut b \leq (q-q1)*b+r.
 cut b \leq r1.
 apply lt_to_not_le r1 b H4 Hcut2.
 elim Hcut.assumption.
-apply trans_le ? ((q-q1)*b) ?.
+apply trans_le ? ((q-q1)*b).
 apply le_times_n.
 apply le_SO_minus.exact H6.
 rewrite < sym_plus.
 apply le_plus_n.
 rewrite < sym_times.
 rewrite > distr_times_minus.
-rewrite > plus_minus ? ? ? ?.
+rewrite > plus_minus.
 rewrite > sym_times.
 rewrite < H3.
 rewrite < sym_times.
@@ -195,6 +192,7 @@ qed.
 theorem div_times: \forall n,m:nat. div ((S n)*m) (S n) = m.
 intros.
 apply div_mod_spec_to_eq ((S n)*m) (S n) ? ? ? O.
+goal 15. (* ?11 is closed with the following tactics *)
 apply div_mod_spec_div_mod.
 simplify.apply le_S_S.apply le_O_n.
 apply div_mod_spec_times.
@@ -276,4 +274,4 @@ apply inj_times_l m.assumption.
 qed.
 
 variant inj_times_l1:\forall n. O < n \to \forall p,q:nat.p*n = q*n \to p=q
-\def lt_O_to_injective_times_l.
\ No newline at end of file
+\def lt_O_to_injective_times_l.