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Diffstat (limited to 'theories/Sorting')
| -rw-r--r-- | theories/Sorting/Permutation.v | 12 |
1 files changed, 12 insertions, 0 deletions
diff --git a/theories/Sorting/Permutation.v b/theories/Sorting/Permutation.v index 026cf32ceb..2f445c341a 100644 --- a/theories/Sorting/Permutation.v +++ b/theories/Sorting/Permutation.v @@ -522,6 +522,18 @@ Proof. repeat red; eauto using Permutation_NoDup. Qed. +Lemma Permutation_repeat x n l : + Permutation l (repeat x n) -> l = repeat x n. +Proof. + revert n; induction l as [|y l IHl] ; simpl; intros n HP; auto. + - now apply Permutation_nil in HP; inversion HP. + - assert (y = x) as Heq by (now apply repeat_spec with n, (Permutation_in _ HP); left); subst. + destruct n; simpl; simpl in HP. + + symmetry in HP; apply Permutation_nil in HP; inversion HP. + + f_equal; apply IHl. + now apply Permutation_cons_inv with x. +Qed. + End Permutation_properties. Section Permutation_map. |