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Diffstat (limited to 'theories/Arith/Factorial.v')
| -rw-r--r-- | theories/Arith/Factorial.v | 14 |
1 files changed, 6 insertions, 8 deletions
diff --git a/theories/Arith/Factorial.v b/theories/Arith/Factorial.v index 3b434b96..37aa1b2c 100644 --- a/theories/Arith/Factorial.v +++ b/theories/Arith/Factorial.v @@ -1,37 +1,35 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Factorial.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - Require Import Plus. Require Import Mult. Require Import Lt. -Open Local Scope nat_scope. +Local Open Scope nat_scope. (** Factorial *) -Boxed Fixpoint fact (n:nat) : nat := +Fixpoint fact (n:nat) : nat := match n with | O => 1 | S n => S n * fact n end. -Arguments Scope fact [nat_scope]. +Arguments fact n%nat. Lemma lt_O_fact : forall n:nat, 0 < fact n. Proof. - simple induction n; unfold lt in |- *; simpl in |- *; auto with arith. + simple induction n; unfold lt; simpl; auto with arith. Qed. Lemma fact_neq_0 : forall n:nat, fact n <> 0. Proof. intro. - apply sym_not_eq. + apply not_eq_sym. apply lt_O_neq. apply lt_O_fact. Qed. |