diff --git a/Batteries/Lean/Name.lean b/Batteries/Lean/Name.lean
index b3705e6a2e..b5530e49d1 100644
--- a/Batteries/Lean/Name.lean
+++ b/Batteries/Lean/Name.lean
@@ -16,8 +16,13 @@ Generally, user code should not explicitly use internal names.
 def isInternalDetail : Name → Bool
   | .str p s     =>
     s.startsWith "_"
-      || s.startsWith "match_"
-      || s.startsWith "proof_"
+      || matchPrefix s "eq_"
+      || matchPrefix s "match_"
+      || matchPrefix s "proof_"
       || p.isInternalOrNum
   | .num _ _     => true
   | p            => p.isInternalOrNum
+where
+  /-- Check that a string begins with the given prefix, and then is only digit characters. -/
+  matchPrefix (s : String) (pre : String) :=
+    s.startsWith pre && (s |>.drop pre.length |>.all Char.isDigit)
diff --git a/Batteries/Util/ExtendedBinder.lean b/Batteries/Util/ExtendedBinder.lean
index 33629b7cc0..d577e1d785 100644
--- a/Batteries/Util/ExtendedBinder.lean
+++ b/Batteries/Util/ExtendedBinder.lean
@@ -52,22 +52,3 @@ macro_rules -- TODO: merging the two macro_rules breaks expansion
   | `(∀ᵉ _ : $ty:term, $b) => `(∀ _ : $ty:term, $b)
   | `(∀ᵉ $x:ident : $ty:term, $b) => `(∀ $x:ident : $ty:term, $b)
   | `(∀ᵉ $x:binderIdent $p:binderPred, $b) => `(∀ $x:binderIdent $p:binderPred, $b)
-
-open Parser.Command in
-/--
-Declares a binder predicate.  For example:
-```
-binder_predicate x " > " y:term => `($x > $y)
-```
--/
-syntax (name := binderPredicate) (docComment)? (Parser.Term.attributes)? (attrKind)?
-  "binder_predicate" optNamedName optNamedPrio ppSpace ident (ppSpace macroArg)* " => "
-    term : command
-
-open Linter.MissingDocs Parser Term in
-/-- Missing docs handler for `binder_predicate` -/
-@[missing_docs_handler binderPredicate]
-def checkBinderPredicate : SimpleHandler := fun stx => do
-  if stx[0].isNone && stx[2][0][0].getKind != ``«local» then
-    if stx[4].isNone then lint stx[3] "binder predicate"
-    else lintNamed stx[4][0][3] "binder predicate"