diff options
Diffstat (limited to 'theories/Arith')
| -rw-r--r-- | theories/Arith/Factorial.v | 15 |
1 files changed, 15 insertions, 0 deletions
diff --git a/theories/Arith/Factorial.v b/theories/Arith/Factorial.v index 4963379e68..71cef55ce4 100644 --- a/theories/Arith/Factorial.v +++ b/theories/Arith/Factorial.v @@ -9,7 +9,10 @@ (*i $Id$ i*) Require Plus. +Require Mult. Require Lt. +V7only [Import nat_scope.]. +Open Local Scope nat_scope. (** Factorial *) @@ -32,3 +35,15 @@ Apply lt_O_neq. Apply lt_O_fact. Qed. +Lemma fact_growing : (m,n:nat) (le m n) -> (le (fact m) (fact n)). +Proof. +NewInduction 1. +Apply le_n. +Assert (le (mult (S O) (fact m)) (mult (S m0) (fact m0))). +Apply le_mult_mult. +Apply lt_le_S; Apply lt_O_Sn. +Assumption. +Simpl (mult (S O) (fact m)) in H0. +Rewrite <- plus_n_O in H0. +Assumption. +Qed. |