diff --git a/midas/checker/registry.py b/midas/checker/registry.py
index db2f972..7ed206d 100644
--- a/midas/checker/registry.py
+++ b/midas/checker/registry.py
@@ -13,6 +13,7 @@ from midas.checker.types import (
     Operation,
     OverloadedFunction,
     Type,
+    TypeVar,
     UnknownType,
     substitute_typevars,
 )
@@ -171,6 +172,11 @@ class TypesRegistry:
             case (Function(), Function()):
                 return self.is_func_subtype(type1, type2)
 
+            case (TypeVar(bound=bound), _):
+                if bound is None:
+                    return False
+                return self.is_subtype(bound, type2)
+
         return False
 
     # TODO: verify the logic in here
diff --git a/midas/checker/types.py b/midas/checker/types.py
index dd8c173..d0dbe2f 100644
--- a/midas/checker/types.py
+++ b/midas/checker/types.py
@@ -191,6 +191,13 @@ def substitute_typevars(type: Type, substitutions: dict[str, Type]) -> Type:
                 ),
             )
 
+        case AppliedType(name=name, args=args, body=body):
+            return AppliedType(
+                name=name,
+                args=[substitute_typevars(arg, substitutions) for arg in args],
+                body=substitute_typevars(body, substitutions),
+            )
+
         case TypeVar(name=name):
             if name in substitutions:
                 return substitutions[name]