diff options
Diffstat (limited to 'theories/Classes/Equivalence.v')
| -rw-r--r-- | theories/Classes/Equivalence.v | 17 |
1 files changed, 11 insertions, 6 deletions
diff --git a/theories/Classes/Equivalence.v b/theories/Classes/Equivalence.v index afdfb4cec..6d550dc93 100644 --- a/theories/Classes/Equivalence.v +++ b/theories/Classes/Equivalence.v @@ -124,10 +124,15 @@ End Respecting. (** The default equivalence on function spaces, with higher-priority than [eq]. *) -Program Instance pointwise_equivalence {A} `(eqb : Equivalence B eqB) : +Instance pointwise_reflexive {A} `(reflb : Reflexive B eqB) : + Reflexive (pointwise_relation A eqB) | 9. +Proof. firstorder. Qed. +Instance pointwise_symmetric {A} `(symb : Symmetric B eqB) : + Symmetric (pointwise_relation A eqB) | 9. +Proof. firstorder. Qed. +Instance pointwise_transitive {A} `(transb : Transitive B eqB) : + Transitive (pointwise_relation A eqB) | 9. +Proof. firstorder. Qed. +Instance pointwise_equivalence {A} `(eqb : Equivalence B eqB) : Equivalence (pointwise_relation A eqB) | 9. - - Next Obligation. - Proof. - transitivity (y a) ; auto. - Qed. +Proof. split; apply _. Qed. |