diff --git a/crates/ty_python_semantic/resources/mdtest/type_properties/satisfied_by_all_typevars.md b/crates/ty_python_semantic/resources/mdtest/type_properties/satisfied_by_all_typevars.md
new file mode 100644
index 0000000000..8d9f563250
--- /dev/null
+++ b/crates/ty_python_semantic/resources/mdtest/type_properties/satisfied_by_all_typevars.md
@@ -0,0 +1,220 @@
+# Constraint set satisfaction
+
+```toml
+[environment]
+python-version = "3.12"
+```
+
+Constraint sets exist to help us check assignability and subtyping of types in the presence of
+typevars. We construct a constraint set describing the conditions under which assignability holds
+between the two types. Then we check whether that constraint set is satisfied for the valid
+specializations of the relevant typevars. This file tests that final step.
+
+## Inferable vs non-inferable typevars
+
+Typevars can appear in _inferable_ or _non-inferable_ positions.
+
+When a typevar is in an inferable position, the constraint set only needs to be satisfied for _some_
+valid specialization. The most common inferable position occurs when invoking a generic function:
+all of the function's typevars are inferable, because we want to use the argument types to infer
+which specialization is being invoked.
+
+When a typevar is in a non-inferable position, the constraint set must be satisfied for _every_
+valid specialization. The most common non-inferable position occurs in the body of a generic
+function or class: here we don't know in advance what type the typevar will be specialized to, and
+so we have to ensure that the body is valid for all possible specializations.
+
+```py
+def f[T](t: T) -> T:
+    # In the function body, T is non-inferable. All assignability checks involving T must be
+    # satisfied for _all_ valid specializations of T.
+    return t
+
+# When invoking the function, T is inferable — we attempt to infer a specialization that is valid
+# for the particular arguments that are passed to the function. Assignability checks (in particular,
+# that the argument type is assignable to the parameter type) only need to succeed for _at least
+# one_ specialization.
+f(1)
+```
+
+In all of the examples below, for ease of reproducibility, we explicitly list the typevars that are
+inferable in each `satisfied_by_all_typevars` call; any typevar not listed is assumed to be
+non-inferable.
+
+## Unbounded typevar
+
+If a typevar has no bound or constraints, then it can specialize to any type. In an inferable
+position, that means we just need a single type (any type at all!) that satisfies the constraint
+set. In a non-inferable position, that means the constraint set must be satisfied for every possible
+type.
+
+```py
+from typing import final, Never
+from ty_extensions import ConstraintSet, static_assert
+
+class Super: ...
+class Base(Super): ...
+class Sub(Base): ...
+
+@final
+class Unrelated: ...
+
+def unbounded[T]():
+    static_assert(ConstraintSet.always().satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(ConstraintSet.always().satisfied_by_all_typevars())
+
+    static_assert(not ConstraintSet.never().satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(not ConstraintSet.never().satisfied_by_all_typevars())
+
+    # (T = Never) is a valid specialization, which satisfies (T ≤ Unrelated).
+    static_assert(ConstraintSet.range(Never, T, Unrelated).satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Base) is a valid specialization, which does not satisfy (T ≤ Unrelated).
+    static_assert(not ConstraintSet.range(Never, T, Unrelated).satisfied_by_all_typevars())
+
+    # (T = Base) is a valid specialization, which satisfies (T ≤ Super).
+    static_assert(ConstraintSet.range(Never, T, Super).satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Unrelated) is a valid specialization, which does not satisfy (T ≤ Super).
+    static_assert(not ConstraintSet.range(Never, T, Super).satisfied_by_all_typevars())
+
+    # (T = Base) is a valid specialization, which satisfies (T ≤ Base).
+    static_assert(ConstraintSet.range(Never, T, Base).satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Unrelated) is a valid specialization, which does not satisfy (T ≤ Base).
+    static_assert(not ConstraintSet.range(Never, T, Base).satisfied_by_all_typevars())
+
+    # (T = Sub) is a valid specialization, which satisfies (T ≤ Sub).
+    static_assert(ConstraintSet.range(Never, T, Sub).satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Unrelated) is a valid specialization, which does not satisfy (T ≤ Sub).
+    static_assert(not ConstraintSet.range(Never, T, Sub).satisfied_by_all_typevars())
+```
+
+## Typevar with an upper bound
+
+If a typevar has an upper bound, then it must specialize to a type that is a subtype of that bound.
+For an inferable typevar, that means we need a single type that satisfies both the constraint set
+and the upper bound. For a non-inferable typevar, that means the constraint set must be satisfied
+for every type that satisfies the upper bound.
+
+```py
+from typing import final, Never
+from ty_extensions import ConstraintSet, static_assert
+
+class Super: ...
+class Base(Super): ...
+class Sub(Base): ...
+
+@final
+class Unrelated: ...
+
+def bounded[T: Base]():
+    static_assert(ConstraintSet.always().satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(ConstraintSet.always().satisfied_by_all_typevars())
+
+    static_assert(not ConstraintSet.never().satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(not ConstraintSet.never().satisfied_by_all_typevars())
+
+    # (T = Base) is a valid specialization, which satisfies (T ≤ Super).
+    static_assert(ConstraintSet.range(Never, T, Super).satisfied_by_all_typevars(inferable=tuple[T]))
+    # Every valid specialization satisfies (T ≤ Base). Since (Base ≤ Super), every valid
+    # specialization also satisfies (T ≤ Super).
+    static_assert(ConstraintSet.range(Never, T, Super).satisfied_by_all_typevars())
+
+    # (T = Base) is a valid specialization, which satisfies (T ≤ Base).
+    static_assert(ConstraintSet.range(Never, T, Base).satisfied_by_all_typevars(inferable=tuple[T]))
+    # Every valid specialization satisfies (T ≤ Base).
+    static_assert(ConstraintSet.range(Never, T, Base).satisfied_by_all_typevars())
+
+    # (T = Sub) is a valid specialization, which satisfies (T ≤ Sub).
+    static_assert(ConstraintSet.range(Never, T, Sub).satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Base) is a valid specialization, which does not satisfy (T ≤ Sub).
+    static_assert(not ConstraintSet.range(Never, T, Sub).satisfied_by_all_typevars())
+
+    # (T = Never) is a valid specialization, which satisfies (T ≤ Unrelated).
+    constraints = ConstraintSet.range(Never, T, Unrelated)
+    static_assert(constraints.satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Base) is a valid specialization, which does not satisfy (T ≤ Unrelated).
+    static_assert(not constraints.satisfied_by_all_typevars())
+
+    # Never is the only type that satisfies both (T ≤ Base) and (T ≤ Unrelated). So there is no
+    # valid specialization that satisfies (T ≤ Unrelated ∧ T ≠ Never).
+    constraints = constraints & ~ConstraintSet.range(Never, T, Never)
+    static_assert(not constraints.satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(not constraints.satisfied_by_all_typevars())
+```
+
+## Constrained typevar
+
+If a typevar has constraints, then it must specialize to one of those specific types. (Not to a
+subtype of one of those types!) For an inferable typevar, that means we need the constraint set to
+be satisfied by any one of the constraints. For a non-inferable typevar, that means we need the
+constraint set to be satisfied by all of those constraints.
+
+```py
+from typing import final, Never
+from ty_extensions import ConstraintSet, static_assert
+
+class Super: ...
+class Base(Super): ...
+class Sub(Base): ...
+
+@final
+class Unrelated: ...
+
+def constrained[T: (Base, Unrelated)]():
+    static_assert(ConstraintSet.always().satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(ConstraintSet.always().satisfied_by_all_typevars())
+
+    static_assert(not ConstraintSet.never().satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(not ConstraintSet.never().satisfied_by_all_typevars())
+
+    # (T = Unrelated) is a valid specialization, which satisfies (T ≤ Unrelated).
+    static_assert(ConstraintSet.range(Never, T, Unrelated).satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Base) is a valid specialization, which does not satisfy (T ≤ Unrelated).
+    static_assert(not ConstraintSet.range(Never, T, Unrelated).satisfied_by_all_typevars())
+
+    # (T = Base) is a valid specialization, which satisfies (T ≤ Super).
+    static_assert(ConstraintSet.range(Never, T, Super).satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Unrelated) is a valid specialization, which does not satisfy (T ≤ Super).
+    static_assert(not ConstraintSet.range(Never, T, Super).satisfied_by_all_typevars())
+
+    # (T = Base) is a valid specialization, which satisfies (T ≤ Base).
+    static_assert(ConstraintSet.range(Never, T, Base).satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Unrelated) is a valid specialization, which does not satisfy (T ≤ Base).
+    static_assert(not ConstraintSet.range(Never, T, Base).satisfied_by_all_typevars())
+
+    # Neither (T = Base) nor (T = Unrelated) satisfy (T ≤ Sub).
+    static_assert(not ConstraintSet.range(Never, T, Sub).satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(not ConstraintSet.range(Never, T, Sub).satisfied_by_all_typevars())
+
+    # (T = Base) and (T = Unrelated) both satisfy (T ≤ Super ∨ T ≤ Unrelated).
+    constraints = ConstraintSet.range(Never, T, Super) | ConstraintSet.range(Never, T, Unrelated)
+    static_assert(constraints.satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(constraints.satisfied_by_all_typevars())
+
+    # (T = Base) and (T = Unrelated) both satisfy (T ≤ Base ∨ T ≤ Unrelated).
+    constraints = ConstraintSet.range(Never, T, Base) | ConstraintSet.range(Never, T, Unrelated)
+    static_assert(constraints.satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(constraints.satisfied_by_all_typevars())
+
+    # (T = Unrelated) is a valid specialization, which satisfies (T ≤ Sub ∨ T ≤ Unrelated).
+    constraints = ConstraintSet.range(Never, T, Sub) | ConstraintSet.range(Never, T, Unrelated)
+    static_assert(constraints.satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Base) is a valid specialization, which does not satisfy (T ≤ Sub ∨ T ≤ Unrelated).
+    static_assert(not constraints.satisfied_by_all_typevars())
+
+    # (T = Unrelated) is a valid specialization, which satisfies (T = Super ∨ T = Unrelated).
+    constraints = ConstraintSet.range(Super, T, Super) | ConstraintSet.range(Unrelated, T, Unrelated)
+    static_assert(constraints.satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Base) is a valid specialization, which does not satisfy (T = Super ∨ T = Unrelated).
+    static_assert(not constraints.satisfied_by_all_typevars())
+
+    # (T = Base) and (T = Unrelated) both satisfy (T = Base ∨ T = Unrelated).
+    constraints = ConstraintSet.range(Base, T, Base) | ConstraintSet.range(Unrelated, T, Unrelated)
+    static_assert(constraints.satisfied_by_all_typevars(inferable=tuple[T]))
+    static_assert(constraints.satisfied_by_all_typevars())
+
+    # (T = Unrelated) is a valid specialization, which satisfies (T = Sub ∨ T = Unrelated).
+    constraints = ConstraintSet.range(Sub, T, Sub) | ConstraintSet.range(Unrelated, T, Unrelated)
+    static_assert(constraints.satisfied_by_all_typevars(inferable=tuple[T]))
+    # (T = Base) is a valid specialization, which does not satisfy (T = Sub ∨ T = Unrelated).
+    static_assert(not constraints.satisfied_by_all_typevars())
+```
diff --git a/crates/ty_python_semantic/src/types.rs b/crates/ty_python_semantic/src/types.rs
index be3816ac12..a4eb563e6a 100644
--- a/crates/ty_python_semantic/src/types.rs
+++ b/crates/ty_python_semantic/src/types.rs
@@ -4161,6 +4161,14 @@ impl<'db> Type<'db> {
                 ))
                 .into()
             }
+            Type::KnownInstance(KnownInstanceType::ConstraintSet(tracked))
+                if name == "satisfied_by_all_typevars" =>
+            {
+                Place::bound(Type::KnownBoundMethod(
+                    KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(tracked),
+                ))
+                .into()
+            }
 
             Type::ClassLiteral(class)
                 if name == "__get__" && class.is_known(db, KnownClass::FunctionType) =>
@@ -6923,6 +6931,7 @@ impl<'db> Type<'db> {
                 | KnownBoundMethodType::ConstraintSetAlways
                 | KnownBoundMethodType::ConstraintSetNever
                 | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_)
+                | KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_)
             )
             | Type::DataclassDecorator(_)
             | Type::DataclassTransformer(_)
@@ -7074,7 +7083,8 @@ impl<'db> Type<'db> {
                 | KnownBoundMethodType::ConstraintSetRange
                 | KnownBoundMethodType::ConstraintSetAlways
                 | KnownBoundMethodType::ConstraintSetNever
-                | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_),
+                | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_)
+                | KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_),
             )
             | Type::DataclassDecorator(_)
             | Type::DataclassTransformer(_)
@@ -10339,6 +10349,7 @@ pub enum KnownBoundMethodType<'db> {
     ConstraintSetAlways,
     ConstraintSetNever,
     ConstraintSetImpliesSubtypeOf(TrackedConstraintSet<'db>),
+    ConstraintSetSatisfiedByAllTypeVars(TrackedConstraintSet<'db>),
 }
 
 pub(super) fn walk_method_wrapper_type<'db, V: visitor::TypeVisitor<'db> + ?Sized>(
@@ -10366,7 +10377,8 @@ pub(super) fn walk_method_wrapper_type<'db, V: visitor::TypeVisitor<'db> + ?Size
         | KnownBoundMethodType::ConstraintSetRange
         | KnownBoundMethodType::ConstraintSetAlways
         | KnownBoundMethodType::ConstraintSetNever
-        | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_) => {}
+        | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_)
+        | KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_) => {}
     }
 }
 
@@ -10434,6 +10446,10 @@ impl<'db> KnownBoundMethodType<'db> {
             | (
                 KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_),
                 KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_),
+            )
+            | (
+                KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_),
+                KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_),
             ) => ConstraintSet::from(true),
 
             (
@@ -10446,7 +10462,8 @@ impl<'db> KnownBoundMethodType<'db> {
                 | KnownBoundMethodType::ConstraintSetRange
                 | KnownBoundMethodType::ConstraintSetAlways
                 | KnownBoundMethodType::ConstraintSetNever
-                | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_),
+                | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_)
+                | KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_),
                 KnownBoundMethodType::FunctionTypeDunderGet(_)
                 | KnownBoundMethodType::FunctionTypeDunderCall(_)
                 | KnownBoundMethodType::PropertyDunderGet(_)
@@ -10456,7 +10473,8 @@ impl<'db> KnownBoundMethodType<'db> {
                 | KnownBoundMethodType::ConstraintSetRange
                 | KnownBoundMethodType::ConstraintSetAlways
                 | KnownBoundMethodType::ConstraintSetNever
-                | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_),
+                | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_)
+                | KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_),
             ) => ConstraintSet::from(false),
         }
     }
@@ -10509,6 +10527,10 @@ impl<'db> KnownBoundMethodType<'db> {
             (
                 KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(left_constraints),
                 KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(right_constraints),
+            )
+            | (
+                KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(left_constraints),
+                KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(right_constraints),
             ) => left_constraints
                 .constraints(db)
                 .iff(db, right_constraints.constraints(db)),
@@ -10523,7 +10545,8 @@ impl<'db> KnownBoundMethodType<'db> {
                 | KnownBoundMethodType::ConstraintSetRange
                 | KnownBoundMethodType::ConstraintSetAlways
                 | KnownBoundMethodType::ConstraintSetNever
-                | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_),
+                | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_)
+                | KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_),
                 KnownBoundMethodType::FunctionTypeDunderGet(_)
                 | KnownBoundMethodType::FunctionTypeDunderCall(_)
                 | KnownBoundMethodType::PropertyDunderGet(_)
@@ -10533,7 +10556,8 @@ impl<'db> KnownBoundMethodType<'db> {
                 | KnownBoundMethodType::ConstraintSetRange
                 | KnownBoundMethodType::ConstraintSetAlways
                 | KnownBoundMethodType::ConstraintSetNever
-                | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_),
+                | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_)
+                | KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_),
             ) => ConstraintSet::from(false),
         }
     }
@@ -10557,7 +10581,8 @@ impl<'db> KnownBoundMethodType<'db> {
             | KnownBoundMethodType::ConstraintSetRange
             | KnownBoundMethodType::ConstraintSetAlways
             | KnownBoundMethodType::ConstraintSetNever
-            | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_) => self,
+            | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_)
+            | KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_) => self,
         }
     }
 
@@ -10573,7 +10598,10 @@ impl<'db> KnownBoundMethodType<'db> {
             KnownBoundMethodType::ConstraintSetRange
             | KnownBoundMethodType::ConstraintSetAlways
             | KnownBoundMethodType::ConstraintSetNever
-            | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_) => KnownClass::ConstraintSet,
+            | KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_)
+            | KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_) => {
+                KnownClass::ConstraintSet
+            }
         }
     }
 
@@ -10712,6 +10740,19 @@ impl<'db> KnownBoundMethodType<'db> {
                     Some(KnownClass::ConstraintSet.to_instance(db)),
                 )))
             }
+
+            KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(_) => {
+                Either::Right(std::iter::once(Signature::new(
+                    Parameters::new([Parameter::keyword_only(Name::new_static("inferable"))
+                        .type_form()
+                        .with_annotated_type(UnionType::from_elements(
+                            db,
+                            [Type::homogeneous_tuple(db, Type::any()), Type::none(db)],
+                        ))
+                        .with_default_type(Type::none(db))]),
+                    Some(KnownClass::Bool.to_instance(db)),
+                )))
+            }
         }
     }
 }
diff --git a/crates/ty_python_semantic/src/types/call/bind.rs b/crates/ty_python_semantic/src/types/call/bind.rs
index 1b4629b301..b0a5cc1b91 100644
--- a/crates/ty_python_semantic/src/types/call/bind.rs
+++ b/crates/ty_python_semantic/src/types/call/bind.rs
@@ -9,6 +9,7 @@ use std::fmt;
 use itertools::{Either, Itertools};
 use ruff_db::parsed::parsed_module;
 use ruff_python_ast::name::Name;
+use rustc_hash::FxHashSet;
 use smallvec::{SmallVec, smallvec, smallvec_inline};
 
 use super::{Argument, CallArguments, CallError, CallErrorKind, InferContext, Signature, Type};
@@ -35,9 +36,10 @@ use crate::types::signatures::{Parameter, ParameterForm, ParameterKind, Paramete
 use crate::types::tuple::{TupleLength, TupleType};
 use crate::types::{
     BoundMethodType, ClassLiteral, DataclassFlags, DataclassParams, FieldInstance,
-    KnownBoundMethodType, KnownClass, KnownInstanceType, MemberLookupPolicy, PropertyInstanceType,
-    SpecialFormType, TrackedConstraintSet, TypeAliasType, TypeContext, UnionBuilder, UnionType,
-    WrapperDescriptorKind, enums, ide_support, infer_isolated_expression, todo_type,
+    KnownBoundMethodType, KnownClass, KnownInstanceType, MemberLookupPolicy, NominalInstanceType,
+    PropertyInstanceType, SpecialFormType, TrackedConstraintSet, TypeAliasType, TypeContext,
+    UnionBuilder, UnionType, WrapperDescriptorKind, enums, ide_support, infer_isolated_expression,
+    todo_type,
 };
 use ruff_db::diagnostic::{Annotation, Diagnostic, SubDiagnostic, SubDiagnosticSeverity};
 use ruff_python_ast::{self as ast, ArgOrKeyword, PythonVersion};
@@ -1174,6 +1176,42 @@ impl<'db> Bindings<'db> {
                         ));
                     }
 
+                    Type::KnownBoundMethod(
+                        KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(tracked),
+                    ) => {
+                        let extract_inferable = |instance: &NominalInstanceType<'db>| {
+                            if instance.has_known_class(db, KnownClass::NoneType) {
+                                // Caller explicitly passed None, so no typevars are inferable.
+                                return Some(FxHashSet::default());
+                            }
+                            instance
+                                .tuple_spec(db)?
+                                .fixed_elements()
+                                .map(|ty| {
+                                    ty.as_typevar()
+                                        .map(|bound_typevar| bound_typevar.identity(db))
+                                })
+                                .collect()
+                        };
+
+                        let inferable = match overload.parameter_types() {
+                            // Caller did not provide argument, so no typevars are inferable.
+                            [None] => FxHashSet::default(),
+                            [Some(Type::NominalInstance(instance))] => {
+                                match extract_inferable(instance) {
+                                    Some(inferable) => inferable,
+                                    None => continue,
+                                }
+                            }
+                            _ => continue,
+                        };
+
+                        let result = tracked
+                            .constraints(db)
+                            .satisfied_by_all_typevars(db, InferableTypeVars::One(&inferable));
+                        overload.set_return_type(Type::BooleanLiteral(result));
+                    }
+
                     Type::ClassLiteral(class) => match class.known(db) {
                         Some(KnownClass::Bool) => match overload.parameter_types() {
                             [Some(arg)] => overload.set_return_type(arg.bool(db).into_type(db)),
diff --git a/crates/ty_python_semantic/src/types/constraints.rs b/crates/ty_python_semantic/src/types/constraints.rs
index ef7632ff2e..ee66cd85f3 100644
--- a/crates/ty_python_semantic/src/types/constraints.rs
+++ b/crates/ty_python_semantic/src/types/constraints.rs
@@ -65,7 +65,10 @@ use salsa::plumbing::AsId;
 
 use crate::Db;
 use crate::types::generics::InferableTypeVars;
-use crate::types::{BoundTypeVarInstance, IntersectionType, Type, TypeRelation, UnionType};
+use crate::types::{
+    BoundTypeVarInstance, IntersectionType, Type, TypeRelation, TypeVarBoundOrConstraints,
+    UnionType,
+};
 
 /// An extension trait for building constraint sets from [`Option`] values.
 pub(crate) trait OptionConstraintsExtension<T> {
@@ -256,6 +259,28 @@ impl<'db> ConstraintSet<'db> {
         }
     }
 
+    /// Returns whether this constraint set is satisfied by all of the typevars that it mentions.
+    ///
+    /// Each typevar has a set of _valid specializations_, which is defined by any upper bound or
+    /// constraints that the typevar has.
+    ///
+    /// Each typevar is also either _inferable_ or _non-inferable_. (You provide a list of the
+    /// `inferable` typevars; all others are considered non-inferable.) For an inferable typevar,
+    /// then there must be _some_ valid specialization that satisfies the constraint set. For a
+    /// non-inferable typevar, then _all_ valid specializations must satisfy it.
+    ///
+    /// Note that we don't have to consider typevars that aren't mentioned in the constraint set,
+    /// since the constraint set cannot be affected by any typevars that it does not mention. That
+    /// means that those additional typevars trivially satisfy the constraint set, regardless of
+    /// whether they are inferable or not.
+    pub(crate) fn satisfied_by_all_typevars(
+        self,
+        db: &'db dyn Db,
+        inferable: InferableTypeVars<'_, 'db>,
+    ) -> bool {
+        self.node.satisfied_by_all_typevars(db, inferable)
+    }
+
     /// Updates this constraint set to hold the union of itself and another constraint set.
     pub(crate) fn union(&mut self, db: &'db dyn Db, other: Self) -> Self {
         self.node = self.node.or(db, other.node);
@@ -746,6 +771,13 @@ impl<'db> Node<'db> {
             .or(db, self.negate(db).and(db, else_node))
     }
 
+    fn satisfies(self, db: &'db dyn Db, other: Self) -> Self {
+        let simplified_self = self.simplify(db);
+        let implication = simplified_self.implies(db, other);
+        let (simplified, domain) = implication.simplify_and_domain(db);
+        simplified.and(db, domain)
+    }
+
     fn when_subtype_of_given(
         self,
         db: &'db dyn Db,
@@ -767,10 +799,48 @@ impl<'db> Node<'db> {
             _ => return lhs.when_subtype_of(db, rhs, inferable).node,
         };
 
-        let simplified_self = self.simplify(db);
-        let implication = simplified_self.implies(db, constraint);
-        let (simplified, domain) = implication.simplify_and_domain(db);
-        simplified.and(db, domain)
+        self.satisfies(db, constraint)
+    }
+
+    fn satisfied_by_all_typevars(
+        self,
+        db: &'db dyn Db,
+        inferable: InferableTypeVars<'_, 'db>,
+    ) -> bool {
+        match self {
+            Node::AlwaysTrue => return true,
+            Node::AlwaysFalse => return false,
+            Node::Interior(_) => {}
+        }
+
+        let mut typevars = FxHashSet::default();
+        self.for_each_constraint(db, &mut |constraint| {
+            typevars.insert(constraint.typevar(db));
+        });
+
+        for typevar in typevars {
+            // Determine which valid specializations of this typevar satisfy the constraint set.
+            let valid_specializations = typevar.valid_specializations(db).node;
+            let when_satisfied = valid_specializations
+                .satisfies(db, self)
+                .and(db, valid_specializations);
+            let satisfied = if typevar.is_inferable(db, inferable) {
+                // If the typevar is inferable, then we only need one valid specialization to
+                // satisfy the constraint set.
+                !when_satisfied.is_never_satisfied()
+            } else {
+                // If the typevar is non-inferable, then we need _all_ valid specializations to
+                // satisfy the constraint set.
+                when_satisfied
+                    .iff(db, valid_specializations)
+                    .is_always_satisfied(db)
+            };
+            if !satisfied {
+                return false;
+            }
+        }
+
+        true
     }
 
     /// Returns a new BDD that returns the same results as `self`, but with some inputs fixed to
@@ -1861,6 +1931,33 @@ impl<'db> SatisfiedClauses<'db> {
     }
 }
 
+/// Returns a constraint set describing the valid specializations of a typevar.
+impl<'db> BoundTypeVarInstance<'db> {
+    pub(crate) fn valid_specializations(self, db: &'db dyn Db) -> ConstraintSet<'db> {
+        match self.typevar(db).bound_or_constraints(db) {
+            None => ConstraintSet::from(true),
+            Some(TypeVarBoundOrConstraints::UpperBound(bound)) => ConstraintSet::constrain_typevar(
+                db,
+                self,
+                Type::Never,
+                bound,
+                TypeRelation::Assignability,
+            ),
+            Some(TypeVarBoundOrConstraints::Constraints(constraints)) => {
+                constraints.elements(db).iter().when_any(db, |constraint| {
+                    ConstraintSet::constrain_typevar(
+                        db,
+                        self,
+                        *constraint,
+                        *constraint,
+                        TypeRelation::Assignability,
+                    )
+                })
+            }
+        }
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/crates/ty_python_semantic/src/types/display.rs b/crates/ty_python_semantic/src/types/display.rs
index 7748dd3ab5..8500c142e8 100644
--- a/crates/ty_python_semantic/src/types/display.rs
+++ b/crates/ty_python_semantic/src/types/display.rs
@@ -535,6 +535,9 @@ impl Display for DisplayRepresentation<'_> {
             Type::KnownBoundMethod(KnownBoundMethodType::ConstraintSetImpliesSubtypeOf(_)) => {
                 f.write_str("bound method `ConstraintSet.implies_subtype_of`")
             }
+            Type::KnownBoundMethod(KnownBoundMethodType::ConstraintSetSatisfiedByAllTypeVars(
+                _,
+            )) => f.write_str("bound method `ConstraintSet.satisfied_by_all_typevars`"),
             Type::WrapperDescriptor(kind) => {
                 let (method, object) = match kind {
                     WrapperDescriptorKind::FunctionTypeDunderGet => ("__get__", "function"),
diff --git a/crates/ty_vendored/ty_extensions/ty_extensions.pyi b/crates/ty_vendored/ty_extensions/ty_extensions.pyi
index 79cda64bef..d23554f0ae 100644
--- a/crates/ty_vendored/ty_extensions/ty_extensions.pyi
+++ b/crates/ty_vendored/ty_extensions/ty_extensions.pyi
@@ -67,6 +67,16 @@ class ConstraintSet:
         .. _subtype: https://typing.python.org/en/latest/spec/concepts.html#subtype-supertype-and-type-equivalence
         """
 
+    def satisfied_by_all_typevars(
+        self, *, inferable: tuple[Any, ...] | None = None
+    ) -> bool:
+        """
+        Returns whether this constraint set is satisfied by all of the typevars
+        that it mentions. You must provide a tuple of the typevars that should
+        be considered `inferable`. All other typevars mentioned in the
+        constraint set will be considered non-inferable.
+        """
+
     def __bool__(self) -> bool: ...
     def __eq__(self, other: ConstraintSet) -> bool: ...
     def __ne__(self, other: ConstraintSet) -> bool: ...