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authorGravatar notin <notin@85f007b7-540e-0410-9357-904b9bb8a0f7>2006-10-17 12:53:34 +0000
committerGravatar notin <notin@85f007b7-540e-0410-9357-904b9bb8a0f7>2006-10-17 12:53:34 +0000
commit28dc7a05cc1d3e03ed1435b3db4340db954a59e2 (patch)
tree63cdf18cd47260eb90550f62f7b22e2e2e208f6c /theories/Arith/Factorial.v
parent744e7f6a319f4d459a3cc2309f575d43041d75aa (diff)
Mise en forme des theories
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@9245 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith/Factorial.v')
-rw-r--r--theories/Arith/Factorial.v32
1 files changed, 16 insertions, 16 deletions
diff --git a/theories/Arith/Factorial.v b/theories/Arith/Factorial.v
index 9f7de8503..8c5315624 100644
--- a/theories/Arith/Factorial.v
+++ b/theories/Arith/Factorial.v
@@ -17,34 +17,34 @@ Open Local Scope nat_scope.
Boxed Fixpoint fact (n:nat) : nat :=
match n with
- | O => 1
- | S n => S n * fact n
+ | O => 1
+ | S n => S n * fact n
end.
Arguments Scope fact [nat_scope].
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 in |- *; simpl in |- *; auto with arith.
Qed.
Lemma fact_neq_0 : forall n:nat, fact n <> 0.
Proof.
-intro.
-apply sym_not_eq.
-apply lt_O_neq.
-apply lt_O_fact.
+ intro.
+ apply sym_not_eq.
+ apply lt_O_neq.
+ apply lt_O_fact.
Qed.
Lemma fact_le : forall n m:nat, n <= m -> fact n <= fact m.
Proof.
-induction 1.
-apply le_n.
-assert (1 * fact n <= S m * fact m).
-apply mult_le_compat.
-apply lt_le_S; apply lt_O_Sn.
-assumption.
-simpl (1 * fact n) in H0.
-rewrite <- plus_n_O in H0.
-assumption.
+ induction 1.
+ apply le_n.
+ assert (1 * fact n <= S m * fact m).
+ apply mult_le_compat.
+ apply lt_le_S; apply lt_O_Sn.
+ assumption.
+ simpl (1 * fact n) in H0.
+ rewrite <- plus_n_O in H0.
+ assumption.
Qed.