diff options
| -rwxr-xr-x | theories/Arith/Le.v | 9 |
1 files changed, 8 insertions, 1 deletions
diff --git a/theories/Arith/Le.v b/theories/Arith/Le.v index 71b020e6ab..c80689836e 100755 --- a/theories/Arith/Le.v +++ b/theories/Arith/Le.v @@ -14,6 +14,13 @@ Open Local Scope nat_scope. Implicit Variables Type m,n,p:nat. +(** Reflexivity *) + +Theorem le_refl : (n:nat)(le n n). +Proof. +Exact le_n. +Qed. + (** Transitivity *) Theorem le_trans : (n,m,p:nat)(le n m)->(le m p)->(le n p). @@ -60,7 +67,7 @@ Elim H ; Simpl ; Auto with arith. Qed. Hints Immediate le_S_n : arith v62. -Lemma le_pred : (n,m:nat)(le n m)->(le (pred n) (pred m)). +Theorem le_pred : (n,m:nat)(le n m)->(le (pred n) (pred m)). Proof. NewInduction n as [|n IHn]. Simpl. Auto with arith. NewDestruct m as [|m]. Simpl. Intro H. Inversion H. |