diff options
Diffstat (limited to 'theories/Relations/Relation_Operators.v')
| -rw-r--r-- | theories/Relations/Relation_Operators.v | 20 |
1 files changed, 14 insertions, 6 deletions
diff --git a/theories/Relations/Relation_Operators.v b/theories/Relations/Relation_Operators.v index 2d1503f23..8fea0abc4 100644 --- a/theories/Relations/Relation_Operators.v +++ b/theories/Relations/Relation_Operators.v @@ -79,7 +79,7 @@ End Reflexive_Transitive_Closure. (** ** Reflexive-symmetric-transitive closure *) -Section Reflexive_Symetric_Transitive_Closure. +Section Reflexive_Symmetric_Transitive_Closure. Variable A : Type. Variable R : relation A. @@ -96,18 +96,18 @@ Section Reflexive_Symetric_Transitive_Closure. (** Alternative definition by symmetric-transitive extension on the left *) Inductive clos_refl_sym_trans_1n (x: A) : A -> Prop := - | rts1n_refl : clos_refl_sym_trans_1n x x - | rts1n_trans (y z:A) : R x y \/ R y x -> + | rst1n_refl : clos_refl_sym_trans_1n x x + | rst1n_trans (y z:A) : R x y \/ R y x -> clos_refl_sym_trans_1n y z -> clos_refl_sym_trans_1n x z. (** Alternative definition by symmetric-transitive extension on the right *) Inductive clos_refl_sym_trans_n1 (x: A) : A -> Prop := - | rtsn1_refl : clos_refl_sym_trans_n1 x x - | rtsn1_trans (y z:A) : R y z \/ R z y -> + | rstn1_refl : clos_refl_sym_trans_n1 x x + | rstn1_trans (y z:A) : R y z \/ R z y -> clos_refl_sym_trans_n1 x y -> clos_refl_sym_trans_n1 x z. -End Reflexive_Symetric_Transitive_Closure. +End Reflexive_Symmetric_Transitive_Closure. (** ** Converse of a relation *) @@ -215,3 +215,11 @@ End Lexicographic_Exponentiation. Hint Unfold transp union: sets v62. Hint Resolve t_step rt_step rt_refl rst_step rst_refl: sets v62. Hint Immediate rst_sym: sets v62. + +(* begin hide *) +(* Compatibility *) +Notation rts1n_refl := rst1n_refl (only parsing). +Notation rts1n_trans := rst1n_trans (only parsing). +Notation rtsn1_refl := rstn1_refl (only parsing). +Notation rtsn1_trans := rstn1_trans (only parsing). +(* end hide *) |