Remove the :> type cast

3 files changed, 2 insertions, 4 deletions

diff --git a/theories/Classes/EquivDec.v b/theories/Classes/EquivDec.v
index a1a4da6f37..575d773c77 100644
--- a/theories/Classes/EquivDec.v
+++ b/theories/Classes/EquivDec.v
@@ -43,7 +43,7 @@ Class EqDec A R {equiv : Equivalence R} :=
    take precedence of [==] defined in the type scope, hence we can have both
    at the same time. *)
 
-Notation " x == y " := (equiv_dec (x :>) (y :>)) (no associativity, at level 70) : equiv_scope.
+Notation " x == y " := (equiv_dec x y) (no associativity, at level 70) : equiv_scope.
 
 Definition swap_sumbool {A B} (x : { A } + { B }) : { B } + { A } :=
   match x with
diff --git a/theories/Classes/SetoidDec.v b/theories/Classes/SetoidDec.v
index f4220e3aa1..435dacbd4c 100644
--- a/theories/Classes/SetoidDec.v
+++ b/theories/Classes/SetoidDec.v
@@ -42,7 +42,7 @@ Class EqDec `(S : Setoid A) :=
    take precedence of [==] defined in the type scope, hence we can have both
    at the same time. *)
 
-Notation " x == y " := (equiv_dec (x :>) (y :>)) (no associativity, at level 70).
+Notation " x == y " := (equiv_dec x y) (no associativity, at level 70).
 
 Definition swap_sumbool {A B} (x : { A } + { B }) : { B } + { A } :=
   match x with
diff --git a/theories/Program/Utils.v b/theories/Program/Utils.v
index b2bdd8099a..717e3191ea 100644
--- a/theories/Program/Utils.v
+++ b/theories/Program/Utils.v
@@ -33,8 +33,6 @@ Notation " `  t " := (proj1_sig t) (at level 10, t at next level) : program_scop
 
 (** Coerces objects to their support before comparing them. *)
 
-Notation " x '`=' y " := ((x :>) = (y :>)) (at level 70) : program_scope.
-
 Require Import Coq.Bool.Sumbool.
 
 (** Construct a dependent disjunction from a boolean. *)