diff options
author | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-10-08 13:39:01 +0000 |
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committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-10-08 13:39:01 +0000 |
commit | 93b74b4be215bd08ca7a123505177d6ec8ac7b4c (patch) | |
tree | cc5b80a8ba038a7c531afae977234f2afdc70699 /theories/ZArith/Znat.v | |
parent | bdec9fddcdaa13800e04e718ffa52f87bddc52d9 (diff) |
Init/Tactics.v: tactic with nicer name 'exfalso' for 'elimtype False'
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12380 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/ZArith/Znat.v')
-rw-r--r-- | theories/ZArith/Znat.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/ZArith/Znat.v b/theories/ZArith/Znat.v index 3d9853ff0..0fc27e38b 100644 --- a/theories/ZArith/Znat.v +++ b/theories/ZArith/Znat.v @@ -66,7 +66,7 @@ Theorem inj_eq_rev : forall n m:nat, Z_of_nat n = Z_of_nat m -> n = m. Proof. intros x y H. destruct (eq_nat_dec x y) as [H'|H']; auto. - elimtype False. + exfalso. exact (inj_neq _ _ H' H). Qed. @@ -111,7 +111,7 @@ Theorem inj_le_rev : forall n m:nat, Z_of_nat n <= Z_of_nat m -> (n <= m)%nat. Proof. intros x y H. destruct (le_lt_dec x y) as [H0|H0]; auto. - elimtype False. + exfalso. assert (H1:=inj_lt _ _ H0). red in H; red in H1. rewrite <- Zcompare_antisym in H; rewrite H1 in H; auto. @@ -121,7 +121,7 @@ Theorem inj_lt_rev : forall n m:nat, Z_of_nat n < Z_of_nat m -> (n < m)%nat. Proof. intros x y H. destruct (le_lt_dec y x) as [H0|H0]; auto. - elimtype False. + exfalso. assert (H1:=inj_le _ _ H0). red in H; red in H1. rewrite <- Zcompare_antisym in H1; rewrite H in H1; auto. @@ -131,7 +131,7 @@ Theorem inj_ge_rev : forall n m:nat, Z_of_nat n >= Z_of_nat m -> (n >= m)%nat. Proof. intros x y H. destruct (le_lt_dec y x) as [H0|H0]; auto. - elimtype False. + exfalso. assert (H1:=inj_gt _ _ H0). red in H; red in H1. rewrite <- Zcompare_antisym in H; rewrite H1 in H; auto. @@ -141,7 +141,7 @@ Theorem inj_gt_rev : forall n m:nat, Z_of_nat n > Z_of_nat m -> (n > m)%nat. Proof. intros x y H. destruct (le_lt_dec x y) as [H0|H0]; auto. - elimtype False. + exfalso. assert (H1:=inj_ge _ _ H0). red in H; red in H1. rewrite <- Zcompare_antisym in H1; rewrite H in H1; auto. |