diff options
Diffstat (limited to 'theories/Wellfounded/Union.v')
| -rw-r--r-- | theories/Wellfounded/Union.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Wellfounded/Union.v b/theories/Wellfounded/Union.v index ebf4ba98e..fbb3d9e3c 100644 --- a/theories/Wellfounded/Union.v +++ b/theories/Wellfounded/Union.v @@ -17,9 +17,9 @@ Require Import Transitive_Closure. Section WfUnion. Variable A : Type. Variables R1 R2 : relation A. - + Notation Union := (union A R1 R2). - + Remark strip_commut : commut A R1 R2 -> forall x y:A, @@ -29,7 +29,7 @@ Section WfUnion. induction 2 as [x y| x y z H0 IH1 H1 IH2]; intros. elim H with y x z; auto with sets; intros x0 H2 H3. exists x0; auto with sets. - + elim IH1 with z0; auto with sets; intros. elim IH2 with x0; auto with sets; intros. exists x1; auto with sets. @@ -50,7 +50,7 @@ Section WfUnion. elim H8; intros. apply H6; auto with sets. apply t_trans with x0; auto with sets. - + elim strip_commut with x x0 y0; auto with sets; intros. apply Acc_inv_trans with x1; auto with sets. unfold union in |- *. @@ -63,7 +63,7 @@ Section WfUnion. apply Acc_intro; auto with sets. Qed. - + Theorem wf_union : commut A R1 R2 -> well_founded R1 -> well_founded R2 -> well_founded Union. Proof. |