diff options
Diffstat (limited to 'src/common')
| -rw-r--r-- | src/common/NonEmpty.v | 11 |
1 files changed, 11 insertions, 0 deletions
diff --git a/src/common/NonEmpty.v b/src/common/NonEmpty.v index cafa7ff..f15bb82 100644 --- a/src/common/NonEmpty.v +++ b/src/common/NonEmpty.v @@ -213,3 +213,14 @@ Inductive norepet {A : Type} : non_empty A -> Prop := | norepet_singleton a : norepet (singleton a) | list_norepet_cons hd tl : ~ In hd tl -> norepet tl -> norepet (hd ::| tl). + +Lemma NEin_NEapp5 : + forall A (a: A) x y, + In a (app x y) -> + In a x \/ In a y. +Proof. + induction x; cbn in *; intros. + - inv H. inv H1. left. constructor. tauto. + - inv H. inv H1. left. constructor; tauto. + apply IHx in H. inv H; intuition (constructor; auto). +Qed. |