diff options
Diffstat (limited to 'theories/Numbers')
| -rw-r--r-- | theories/Numbers/Natural/Abstract/NBase.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/NumPrelude.v | 4 |
2 files changed, 3 insertions, 3 deletions
diff --git a/theories/Numbers/Natural/Abstract/NBase.v b/theories/Numbers/Natural/Abstract/NBase.v index fc2cc81ebd..1a11f7a131 100644 --- a/theories/Numbers/Natural/Abstract/NBase.v +++ b/theories/Numbers/Natural/Abstract/NBase.v @@ -81,7 +81,7 @@ function (by recursion) that maps 0 to false and the successor to true *) Definition if_zero (A : Set) (a b : A) (n : N) : A := recursion a (fun _ _ => b) n. -Add Morphism (if_zero A) with signature ((@eq (A:Set)) ==> (@eq A) ==> Neq ==> (@eq A)) as if_zero_wd. +Add Parametric Morphism (A : Set) : (if_zero A) with signature (@eq _ ==> @eq _ ==> Neq ==> @eq _) as if_zero_wd. Proof. intros; unfold if_zero. apply recursion_wd with (Aeq := (@eq A)). reflexivity. unfold fun2_eq; now intros. assumption. diff --git a/theories/Numbers/NumPrelude.v b/theories/Numbers/NumPrelude.v index c063c7bc1d..f042ab0685 100644 --- a/theories/Numbers/NumPrelude.v +++ b/theories/Numbers/NumPrelude.v @@ -148,13 +148,13 @@ intros R1 R2 R3 H1 H2 x y; rewrite H1; apply H2. now symmetry. Qed. -Add Relation (A -> B -> Prop) (@relations_eq A B) +Add Parametric Relation (A B : Type) : (A -> B -> Prop) (@relations_eq A B) reflexivity proved by (proj1 (relations_eq_equiv A B)) symmetry proved by (proj2 (proj2 (relations_eq_equiv A B))) transitivity proved by (proj1 (proj2 (relations_eq_equiv A B))) as relations_eq_rel. -Add Morphism (@well_founded A) with signature (@relations_eq A A) ==> iff as well_founded_wd. +Add Parametric Morphism (A : Type) : (@well_founded A) with signature (@relations_eq A A) ==> iff as well_founded_wd. Proof. unfold relations_eq, well_founded; intros R1 R2 H; split; intros H1 a; induction (H1 a) as [x H2 H3]; constructor; |