diff options
Diffstat (limited to 'theories/Relations')
| -rw-r--r-- | theories/Relations/Operators_Properties.v | 2 | ||||
| -rw-r--r-- | theories/Relations/Relation_Operators.v | 10 |
2 files changed, 6 insertions, 6 deletions
diff --git a/theories/Relations/Operators_Properties.v b/theories/Relations/Operators_Properties.v index 22582f75d..2ced22298 100644 --- a/theories/Relations/Operators_Properties.v +++ b/theories/Relations/Operators_Properties.v @@ -70,7 +70,7 @@ Section Properties. apply Build_equivalence. exact (rst_refl A R). exact (rst_trans A R). - exact (fun x y => rst_sym A R y x). + exact (rst_sym A R). Qed. (** Idempotency of the reflexive-symmetric-transitive closure operator *) diff --git a/theories/Relations/Relation_Operators.v b/theories/Relations/Relation_Operators.v index 2793da5b1..eec3f8ebd 100644 --- a/theories/Relations/Relation_Operators.v +++ b/theories/Relations/Relation_Operators.v @@ -85,11 +85,11 @@ Section Reflexive_Symetric_Transitive_Closure. (** Definition by direct reflexive-symmetric-transitive closure *) - Inductive clos_refl_sym_trans (x:A) : A -> Prop := - | rst_step (y:A) : R x y -> clos_refl_sym_trans x y - | rst_refl : clos_refl_sym_trans x x - | rst_sym (y:A) : clos_refl_sym_trans y x -> clos_refl_sym_trans x y - | rst_trans (y z:A) : + Inductive clos_refl_sym_trans : relation A := + | rst_step (x y:A) : R x y -> clos_refl_sym_trans x y + | rst_refl (x:A) : clos_refl_sym_trans x x + | rst_sym (x y:A) : clos_refl_sym_trans x y -> clos_refl_sym_trans y x + | rst_trans (x y z:A) : clos_refl_sym_trans x y -> clos_refl_sym_trans y z -> clos_refl_sym_trans x z. |