This commit is contained in:
Thomas Baruchel 2023-01-04 19:32:01 +01:00
parent e845183004
commit 79f9525fbd

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@ -1138,45 +1138,43 @@ Proof.
rewrite H5 in H9. rewrite Nat.add_cancel_l in H9.
destruct b; destruct b0.
reflexivity.
rewrite count_occ_app in H9. rewrite count_occ_app in H9.
rewrite count_occ_cons_eq in H9. rewrite count_occ_cons_neq in H9.
rewrite count_occ_nil in H9. rewrite count_occ_nil in H9.
rewrite Nat.add_1_r in H9. rewrite Nat.add_0_r in H9.
rewrite count_occ_app in H5. rewrite count_occ_app in H5.
rewrite count_occ_cons_neq in H5. rewrite count_occ_cons_eq in H5.
rewrite count_occ_nil in H5. rewrite count_occ_nil in H5.
rewrite Nat.add_1_r in H5. rewrite Nat.add_0_r in H5.
rewrite H5 in H9.
rewrite <- Nat.add_1_r in H9. rewrite <- Nat.add_1_r in H9.
rewrite <- Nat.add_0_r in H9. rewrite <- Nat.add_assoc in H9.
rewrite Nat.add_cancel_l in H9. inversion H9.
reflexivity. easy. easy. reflexivity.
rewrite count_occ_app in H9. rewrite count_occ_app in H9.
rewrite count_occ_cons_neq in H9. rewrite count_occ_cons_eq in H9.
rewrite count_occ_nil in H9. rewrite count_occ_nil in H9.
rewrite Nat.add_1_r in H9. rewrite Nat.add_0_r in H9.
rewrite count_occ_app in H5. rewrite count_occ_app in H5.
rewrite count_occ_cons_eq in H5. rewrite count_occ_cons_neq in H5.
rewrite count_occ_nil in H5. rewrite count_occ_nil in H5.
rewrite Nat.add_1_r in H5. rewrite Nat.add_0_r in H5.
rewrite <- H5 in H9.
rewrite <- Nat.add_1_r in H9. rewrite <- Nat.add_1_r in H9.
rewrite <- Nat.add_0_r in H9 at 1. rewrite <- Nat.add_assoc in H9.
rewrite Nat.add_cancel_l in H9. inversion H9.
easy. reflexivity. reflexivity. easy.
reflexivity.
rewrite app_assoc_reverse. apply app_inv_head_iff.
rewrite app_assoc_reverse. rewrite app_assoc_reverse.
rewrite app_assoc_reverse. rewrite app_assoc_reverse.
apply app_inv_head_iff. apply app_inv_head_iff.
rewrite app_assoc_reverse.
apply app_inv_head_iff. apply app_inv_head_iff.
rewrite app_assoc_reverse.
reflexivity.
reflexivity.
+ reflexivity.
+ rewrite count_occ_app in H9. rewrite count_occ_app in H9.
rewrite count_occ_cons_eq in H9. rewrite count_occ_cons_neq in H9.
rewrite count_occ_nil in H9. rewrite count_occ_nil in H9.
rewrite Nat.add_1_r in H9. rewrite Nat.add_0_r in H9.
rewrite count_occ_app in H5. rewrite count_occ_app in H5.
rewrite count_occ_cons_neq in H5. rewrite count_occ_cons_eq in H5.
rewrite count_occ_nil in H5. rewrite count_occ_nil in H5.
rewrite Nat.add_1_r in H5. rewrite Nat.add_0_r in H5.
rewrite H5 in H9.
rewrite <- Nat.add_1_r in H9. rewrite <- Nat.add_1_r in H9.
rewrite <- Nat.add_0_r in H9. rewrite <- Nat.add_assoc in H9.
rewrite Nat.add_cancel_l in H9. inversion H9.
reflexivity. easy. easy. reflexivity.
+ rewrite count_occ_app in H9. rewrite count_occ_app in H9.
rewrite count_occ_cons_neq in H9. rewrite count_occ_cons_eq in H9.
rewrite count_occ_nil in H9. rewrite count_occ_nil in H9.
rewrite Nat.add_1_r in H9. rewrite Nat.add_0_r in H9.
rewrite count_occ_app in H5. rewrite count_occ_app in H5.
rewrite count_occ_cons_eq in H5. rewrite count_occ_cons_neq in H5.
rewrite count_occ_nil in H5. rewrite count_occ_nil in H5.
rewrite Nat.add_1_r in H5. rewrite Nat.add_0_r in H5.
rewrite <- H5 in H9.
rewrite <- Nat.add_1_r in H9. rewrite <- Nat.add_1_r in H9.
rewrite <- Nat.add_0_r in H9 at 1. rewrite <- Nat.add_assoc in H9.
rewrite Nat.add_cancel_l in H9. inversion H9.
easy. reflexivity. reflexivity. easy.
+ reflexivity.
+ rewrite app_assoc_reverse. apply app_inv_head_iff.
rewrite app_assoc_reverse. rewrite app_assoc_reverse.
rewrite app_assoc_reverse. rewrite app_assoc_reverse.
apply app_inv_head_iff. apply app_inv_head_iff.
rewrite app_assoc_reverse.
apply app_inv_head_iff. apply app_inv_head_iff.
rewrite app_assoc_reverse.
reflexivity.
+ reflexivity.
Qed.