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Diffstat (limited to 'src/common/NonEmpty.v')
| -rw-r--r-- | src/common/NonEmpty.v | 12 |
1 files changed, 12 insertions, 0 deletions
diff --git a/src/common/NonEmpty.v b/src/common/NonEmpty.v index 2169306..24a29a3 100644 --- a/src/common/NonEmpty.v +++ b/src/common/NonEmpty.v @@ -326,3 +326,15 @@ Proof. - constructor. - clear H. inv H1; intuition (constructor; auto). Qed. + +Lemma In_map2 : + forall A B (f: A -> B) n (x: B), + In x (map f n) -> + exists y, In y n /\ x = f y. +Proof. + induction n; inversion 1; subst; cbn in *. + - inv H. exists a; split; auto. constructor. + - clear H. inv H1. + + exists a; split; auto; constructor; tauto. + + exploit IHn; eauto; simplify. exists x0; split; auto; constructor; tauto. +Qed. |