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| author | Olivier Laurent | 2020-08-07 18:55:46 +0200 |
|---|---|---|
| committer | Olivier Laurent | 2020-08-12 12:06:49 +0200 |
| commit | 94bb6fa0152ea61661f2e5d990f8d46cbdcdf9cf (patch) | |
| tree | bbec8fc8d1dbe8ab7e77a0777c0dfb9b0bacd919 /theories/Sorting | |
| parent | 7427e7c5fa5312e7625ebf5243978691fdb04f92 (diff) | |
Additional statements about List.repeat
Co-authored-by: Anton Trunov <anton.a.trunov@gmail.com>
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. |