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This commit is contained in:
Thomas Baruchel 2023-10-21 15:33:27 +02:00
parent 1e18bbe495
commit 836232e28e
1 changed files with 5 additions and 8 deletions
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13
src/permutations.v
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@ -169,9 +169,8 @@ Proof.
assert (incl ([length (l1++l2)]++l2++l1) (l1++[length (l1++l2)]++l2)).
unfold incl. intro a. intro J. rewrite app_assoc in J.
rewrite in_app_iff. rewrite in_app_iff in J. destruct J.
right. assumption. left. assumption.
apply incl_app_inv in H0. destruct H0. apply incl_app_inv in H1.
destruct H1.
right. assumption. left. assumption. apply incl_app_inv in H0.
destruct H0. apply incl_app_inv in H1. destruct H1.
assert (incl (l1++l2) (l1 ++ [length (l1 ++ l2)] ++ l2)).
apply incl_app; assumption.
assert (incl ([length (l1++l2)]++l1++l2) (l1 ++ [length (l1 ++ l2)] ++ l2)).
@ -184,11 +183,9 @@ Proof.
apply incl_app. easy.
apply perm_seq_1 in H. rewrite app_length in H. simpl in H.
rewrite Nat.add_succ_r in H. rewrite seq_S in H. apply incl_app_inv in H.
destruct H. rewrite app_length at 1. assumption.
easy. apply Add_app.
unfold incl in I. unfold permutation.
intro k. intro. apply I. apply in_seq.
split. apply Nat.le_0_l. assumption.
destruct H. rewrite app_length at 1. assumption. easy. apply Add_app.
unfold incl in I. unfold permutation. intro k. intro.
apply I. apply in_seq. split. apply Nat.le_0_l. assumption.
Qed.