diff options
Diffstat (limited to 'theories/Sorting')
| -rw-r--r-- | theories/Sorting/CPermutation.v | 5 | ||||
| -rw-r--r-- | theories/Sorting/Permutation.v | 19 |
2 files changed, 11 insertions, 13 deletions
diff --git a/theories/Sorting/CPermutation.v b/theories/Sorting/CPermutation.v index 21d04da877..31d9f7f0ed 100644 --- a/theories/Sorting/CPermutation.v +++ b/theories/Sorting/CPermutation.v @@ -235,9 +235,8 @@ induction m as [| b m]; intros l HC. apply CPermutation_nil in HC; inversion HC. - symmetry in HC. destruct (CPermutation_vs_cons_inv HC) as [m1 [m2 [-> Heq]]]. - apply map_eq_app in Heq as [l1 [l1' [-> [-> Heq]]]]. - symmetry in Heq. - apply map_eq_cons in Heq as [a [l1'' [-> [-> ->]]]]. + apply map_eq_app in Heq as [l1 [l1' [-> [<- Heq]]]]. + apply map_eq_cons in Heq as [a [l1'' [-> [<- <-]]]]. exists (a :: l1'' ++ l1); split. + now simpl; rewrite map_app. + now rewrite app_comm_cons. diff --git a/theories/Sorting/Permutation.v b/theories/Sorting/Permutation.v index ffef8a216d..026cf32ceb 100644 --- a/theories/Sorting/Permutation.v +++ b/theories/Sorting/Permutation.v @@ -273,8 +273,8 @@ Proof. exact Permutation_length. Qed. -Instance Permutation_Forall (P : A -> Prop) : - Proper ((@Permutation A) ==> Basics.impl) (Forall P). +Global Instance Permutation_Forall (P : A -> Prop) : + Proper ((@Permutation A) ==> Basics.impl) (Forall P) | 10. Proof. intros l1 l2 HP. induction HP; intro HF; auto. @@ -283,8 +283,8 @@ Proof. inversion_clear HF2; auto. Qed. -Instance Permutation_Exists (P : A -> Prop) : - Proper ((@Permutation A) ==> Basics.impl) (Exists P). +Global Instance Permutation_Exists (P : A -> Prop) : + Proper ((@Permutation A) ==> Basics.impl) (Exists P) | 10. Proof. intros l1 l2 HP. induction HP; intro HF; auto. @@ -552,7 +552,6 @@ Proof. - symmetry in HP. destruct (Permutation_vs_cons_inv HP) as [l3 [l4 Heq]]. destruct (map_eq_app _ _ _ _ Heq) as [l1' [l2' [Heq1 [Heq2 Heq3]]]]; subst. - symmetry in Heq3. destruct (map_eq_cons _ _ Heq3) as [b [l1'' [Heq1' [Heq2' Heq3']]]]; subst. rewrite map_app in HP; simpl in HP. symmetry in HP. @@ -582,8 +581,8 @@ Proof. now contradiction (Hf x). Qed. -Instance Permutation_flat_map (g : A -> list B) : - Proper ((@Permutation A) ==> (@Permutation B)) (flat_map g). +Global Instance Permutation_flat_map (g : A -> list B) : + Proper ((@Permutation A) ==> (@Permutation B)) (flat_map g) | 10. Proof. intros l1; induction l1; intros l2 HP. - now apply Permutation_nil in HP; subst. @@ -774,7 +773,7 @@ Qed. End Permutation_alt. -Instance Permutation_list_sum : Proper (@Permutation nat ==> eq) list_sum. +Instance Permutation_list_sum : Proper (@Permutation nat ==> eq) list_sum | 10. Proof. intros l1 l2 HP; induction HP; simpl; intuition. - rewrite 2 (Nat.add_comm x). @@ -782,7 +781,7 @@ Proof. - now transitivity (list_sum l'). Qed. -Instance Permutation_list_max : Proper (@Permutation nat ==> eq) list_max. +Instance Permutation_list_max : Proper (@Permutation nat ==> eq) list_max | 10. Proof. intros l1 l2 HP; induction HP; simpl; intuition. - rewrite 2 (Nat.max_comm x). @@ -807,7 +806,7 @@ Proof. now apply (perm_t_trans IHHP2). Qed. -Instance Permutation_transp_equiv : Equivalence Permutation_transp. +Global Instance Permutation_transp_equiv : Equivalence Permutation_transp | 100. Proof. split. - intros l; apply perm_t_refl. |