diff --git a/core/array.rbs b/core/array.rbs
index 25ce493b5..03d3f13a6 100644
--- a/core/array.rbs
+++ b/core/array.rbs
@@ -2215,7 +2215,7 @@ class Array[unchecked out Elem] < Object
   #
   # Related: see [Methods for Querying](rdoc-ref:Array@Methods+for+Querying).
   #
-  def include?: (Elem object) -> bool
+  def include?: (top object) -> bool
 
   # <!-- rdoc-file=array.c -->
   # Returns the zero-based integer index of a specified element, or `nil`.
diff --git a/core/enumerable.rbs b/core/enumerable.rbs
index 4543e0959..d7531f153 100644
--- a/core/enumerable.rbs
+++ b/core/enumerable.rbs
@@ -816,7 +816,7 @@ module Enumerable[unchecked out Elem] : _Each[Elem]
   #     {foo: 0, bar: 1, baz: 2}.include?('foo') # => false
   #     {foo: 0, bar: 1, baz: 2}.include?(0)     # => false
   #
-  def include?: (Elem arg0) -> bool
+  def include?: (top arg0) -> bool
 
   # <!--
   #   rdoc-file=enum.c
@@ -1663,7 +1663,7 @@ module Enumerable[unchecked out Elem] : _Each[Elem]
   #     {foo: 0, bar: 1, baz: 2}.include?('foo') # => false
   #     {foo: 0, bar: 1, baz: 2}.include?(0)     # => false
   #
-  def member?: (Elem arg0) -> bool
+  def member?: (top arg0) -> bool
 
   # <!-- rdoc-file=enum.c -->
   # Returns the result of applying a reducer to an initial value and the first
diff --git a/core/hash.rbs b/core/hash.rbs
index 36a7268bb..0a56bb66f 100644
--- a/core/hash.rbs
+++ b/core/hash.rbs
@@ -1267,7 +1267,7 @@ class Hash[unchecked out K, unchecked out V] < Object
   #
   # Related: [Methods for Querying](rdoc-ref:Hash@Methods+for+Querying).
   #
-  def has_key?: (K arg0) -> bool
+  def has_key?: (_Key) -> bool
 
   # <!--
   #   rdoc-file=hash.c
@@ -1277,7 +1277,7 @@ class Hash[unchecked out K, unchecked out V] < Object
   #
   # Related: [Methods for Querying](rdoc-ref:Hash@Methods+for+Querying).
   #
-  def has_value?: (V arg0) -> bool
+  def has_value?: (top arg0) -> bool
 
   # <!--
   #   rdoc-file=hash.c
diff --git a/core/set.rbs b/core/set.rbs
index 4adcb0fa6..cecad36d8 100644
--- a/core/set.rbs
+++ b/core/set.rbs
@@ -356,7 +356,7 @@ class Set[unchecked out A]
   #
   # See also Enumerable#include?
   #
-  def include?: (A) -> bool
+  def include?: (Hash::_Key) -> bool
 
   # <!-- rdoc-file=set.c -->
   # Returns true if the set contains the given object: