diff options
author | notin <notin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2006-10-17 12:53:34 +0000 |
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committer | notin <notin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2006-10-17 12:53:34 +0000 |
commit | 28dc7a05cc1d3e03ed1435b3db4340db954a59e2 (patch) | |
tree | 63cdf18cd47260eb90550f62f7b22e2e2e208f6c /theories/Arith/Compare.v | |
parent | 744e7f6a319f4d459a3cc2309f575d43041d75aa (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/Compare.v')
-rw-r--r-- | theories/Arith/Compare.v | 26 |
1 files changed, 11 insertions, 15 deletions
diff --git a/theories/Arith/Compare.v b/theories/Arith/Compare.v index 222367b74..77fa80539 100644 --- a/theories/Arith/Compare.v +++ b/theories/Arith/Compare.v @@ -9,13 +9,9 @@ (*i $Id$ i*) (** Equality is decidable on [nat] *) + Open Local Scope nat_scope. -(* -Lemma not_eq_sym : (A:Set)(p,q:A)(~p=q) -> ~(q=p). -Proof sym_not_eq. -Hints Immediate not_eq_sym : arith. -*) Notation not_eq_sym := sym_not_eq. Implicit Types m n p q : nat. @@ -41,17 +37,17 @@ Proof le_lt_or_eq. (* By special request of G. Kahn - Used in Group Theory *) Lemma discrete_nat : - forall n m, n < m -> S n = m \/ (exists r : nat, m = S (S (n + r))). + forall n m, n < m -> S n = m \/ (exists r : nat, m = S (S (n + r))). Proof. -intros m n H. -lapply (lt_le_S m n); auto with arith. -intro H'; lapply (le_lt_or_eq (S m) n); auto with arith. -induction 1; auto with arith. -right; exists (n - S (S m)); simpl in |- *. -rewrite (plus_comm m (n - S (S m))). -rewrite (plus_n_Sm (n - S (S m)) m). -rewrite (plus_n_Sm (n - S (S m)) (S m)). -rewrite (plus_comm (n - S (S m)) (S (S m))); auto with arith. + intros m n H. + lapply (lt_le_S m n); auto with arith. + intro H'; lapply (le_lt_or_eq (S m) n); auto with arith. + induction 1; auto with arith. + right; exists (n - S (S m)); simpl in |- *. + rewrite (plus_comm m (n - S (S m))). + rewrite (plus_n_Sm (n - S (S m)) m). + rewrite (plus_n_Sm (n - S (S m)) (S m)). + rewrite (plus_comm (n - S (S m)) (S (S m))); auto with arith. Qed. Require Export Wf_nat. |