new version of div_and_mod

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

diff --git a/matita/library/nat/lt_arith.ma b/matita/library/nat/lt_arith.ma
index f60da5eba31f2c07d7b53c70d62c231d362c2208..6635a8b0da4f5dc1f22191dbba8bf75b966a7aaf 100644 (file)
--- a/matita/library/nat/lt_arith.ma
+++ b/matita/library/nat/lt_arith.ma
@@ -30,7 +30,7 @@ monotonic_lt_plus_r.
 
 theorem monotonic_lt_plus_l: 
 \forall n:nat.monotonic nat lt (\lambda m.m+n).
-change with (\forall n,p,q:nat. p < q \to p + n < q + n).
+simplify.
 intros.
 rewrite < sym_plus. rewrite < (sym_plus n).
 apply lt_plus_r.assumption.
@@ -71,10 +71,9 @@ qed.
 (* times *)
 theorem monotonic_lt_times_r: 
 \forall n:nat.monotonic nat lt (\lambda m.(S n)*m).
-change with (\forall n,p,q:nat. p < q \to (S n) * p < (S n) * q).
+simplify.
 intros.elim n.
 simplify.rewrite < plus_n_O.rewrite < plus_n_O.assumption.
-change with (p + (S n1) * p < q + (S n1) * q).
 apply lt_plus.assumption.assumption.
 qed.
 
@@ -83,10 +82,9 @@ theorem lt_times_r: \forall n,p,q:nat. p < q \to (S n) * p < (S n) * q
 
 theorem monotonic_lt_times_l: 
 \forall m:nat.monotonic nat lt (\lambda n.n * (S m)).
-change with 
-(\forall n,p,q:nat. p < q \to p*(S n) < q*(S n)).
+simplify.
 intros.
-rewrite < sym_times.rewrite < (sym_times (S n)).
+rewrite < sym_times.rewrite < (sym_times (S m)).
 apply lt_times_r.assumption.
 qed.