diff --git a/src/Type/Accessory/AccessoryArrayListType.php b/src/Type/Accessory/AccessoryArrayListType.php
index 0be2c190c8..d6624108f2 100644
--- a/src/Type/Accessory/AccessoryArrayListType.php
+++ b/src/Type/Accessory/AccessoryArrayListType.php
@@ -76,14 +76,19 @@ public function getConstantStrings(): array
 
 	public function accepts(Type $type, bool $strictTypes): AcceptsResult
 	{
+		$isArray = $type->isArray();
+		$isList = $type->isList();
+		$isListArray = $isArray->and($isList);
+
+		if ($isListArray->yes()) {
+			return AcceptsResult::createYes();
+		}
+
 		if ($type instanceof CompoundType) {
 			return $type->isAcceptedBy($this, $strictTypes);
 		}
 
-		$isArray = $type->isArray();
-		$isList = $type->isList();
-
-		return new AcceptsResult($isArray->and($isList), []);
+		return new AcceptsResult($isListArray, []);
 	}
 
 	public function isSuperTypeOf(Type $type): IsSuperTypeOfResult
diff --git a/src/Type/Accessory/AccessoryLiteralStringType.php b/src/Type/Accessory/AccessoryLiteralStringType.php
index 63791b6619..abf0b2cbc4 100644
--- a/src/Type/Accessory/AccessoryLiteralStringType.php
+++ b/src/Type/Accessory/AccessoryLiteralStringType.php
@@ -74,11 +74,17 @@ public function accepts(Type $type, bool $strictTypes): AcceptsResult
 		if ($type instanceof MixedType) {
 			return AcceptsResult::createNo();
 		}
+
+		$isLiteralString = $type->isLiteralString();
+		if ($isLiteralString->yes()) {
+			return AcceptsResult::createYes();
+		}
+
 		if ($type instanceof CompoundType) {
 			return $type->isAcceptedBy($this, $strictTypes);
 		}
 
-		return new AcceptsResult($type->isLiteralString(), []);
+		return new AcceptsResult($isLiteralString, []);
 	}
 
 	public function isSuperTypeOf(Type $type): IsSuperTypeOfResult
diff --git a/src/Type/Accessory/AccessoryLowercaseStringType.php b/src/Type/Accessory/AccessoryLowercaseStringType.php
index 4e9a014b32..13ce997f52 100644
--- a/src/Type/Accessory/AccessoryLowercaseStringType.php
+++ b/src/Type/Accessory/AccessoryLowercaseStringType.php
@@ -71,11 +71,17 @@ public function getConstantStrings(): array
 
 	public function accepts(Type $type, bool $strictTypes): AcceptsResult
 	{
+		$isLowercaseString = $type->isLowercaseString();
+
+		if ($isLowercaseString->yes()) {
+			return AcceptsResult::createYes();
+		}
+
 		if ($type instanceof CompoundType) {
 			return $type->isAcceptedBy($this, $strictTypes);
 		}
 
-		return new AcceptsResult($type->isLowercaseString(), []);
+		return new AcceptsResult($isLowercaseString, []);
 	}
 
 	public function isSuperTypeOf(Type $type): IsSuperTypeOfResult
diff --git a/src/Type/Accessory/AccessoryNonEmptyStringType.php b/src/Type/Accessory/AccessoryNonEmptyStringType.php
index c77cfeaefa..a635ea8618 100644
--- a/src/Type/Accessory/AccessoryNonEmptyStringType.php
+++ b/src/Type/Accessory/AccessoryNonEmptyStringType.php
@@ -72,14 +72,17 @@ public function getConstantStrings(): array
 
 	public function accepts(Type $type, bool $strictTypes): AcceptsResult
 	{
-		if ($type->isNonEmptyString()->yes()) {
+		$isNonEmptyString = $type->isNonEmptyString();
+
+		if ($isNonEmptyString->yes()) {
 			return AcceptsResult::createYes();
 		}
+
 		if ($type instanceof CompoundType) {
 			return $type->isAcceptedBy($this, $strictTypes);
 		}
 
-		return new AcceptsResult($type->isNonEmptyString(), []);
+		return new AcceptsResult($isNonEmptyString, []);
 	}
 
 	public function isSuperTypeOf(Type $type): IsSuperTypeOfResult
diff --git a/src/Type/Accessory/AccessoryNonFalsyStringType.php b/src/Type/Accessory/AccessoryNonFalsyStringType.php
index 65f3fe0919..dc5548789a 100644
--- a/src/Type/Accessory/AccessoryNonFalsyStringType.php
+++ b/src/Type/Accessory/AccessoryNonFalsyStringType.php
@@ -74,11 +74,17 @@ public function getConstantStrings(): array
 
 	public function accepts(Type $type, bool $strictTypes): AcceptsResult
 	{
+		$isNonFalsyString = $type->isNonFalsyString();
+
+		if ($isNonFalsyString->yes()) {
+			return AcceptsResult::createYes();
+		}
+
 		if ($type instanceof CompoundType) {
 			return $type->isAcceptedBy($this, $strictTypes);
 		}
 
-		return new AcceptsResult($type->isNonFalsyString(), []);
+		return new AcceptsResult($isNonFalsyString, []);
 	}
 
 	public function isSuperTypeOf(Type $type): IsSuperTypeOfResult
diff --git a/src/Type/Accessory/AccessoryNumericStringType.php b/src/Type/Accessory/AccessoryNumericStringType.php
index 5fe7ae79af..625c82675d 100644
--- a/src/Type/Accessory/AccessoryNumericStringType.php
+++ b/src/Type/Accessory/AccessoryNumericStringType.php
@@ -71,11 +71,17 @@ public function getConstantStrings(): array
 
 	public function accepts(Type $type, bool $strictTypes): AcceptsResult
 	{
+		$isNumericString = $type->isNumericString();
+
+		if ($isNumericString->yes()) {
+			return AcceptsResult::createYes();
+		}
+
 		if ($type instanceof CompoundType) {
 			return $type->isAcceptedBy($this, $strictTypes);
 		}
 
-		return new AcceptsResult($type->isNumericString(), []);
+		return new AcceptsResult($isNumericString, []);
 	}
 
 	public function isSuperTypeOf(Type $type): IsSuperTypeOfResult
diff --git a/src/Type/Accessory/AccessoryUppercaseStringType.php b/src/Type/Accessory/AccessoryUppercaseStringType.php
index 607aefabdc..f4f63666fe 100644
--- a/src/Type/Accessory/AccessoryUppercaseStringType.php
+++ b/src/Type/Accessory/AccessoryUppercaseStringType.php
@@ -71,11 +71,17 @@ public function getConstantStrings(): array
 
 	public function accepts(Type $type, bool $strictTypes): AcceptsResult
 	{
+		$isUppercaseString = $type->isUppercaseString();
+
+		if ($isUppercaseString->yes()) {
+			return AcceptsResult::createYes();
+		}
+
 		if ($type instanceof CompoundType) {
 			return $type->isAcceptedBy($this, $strictTypes);
 		}
 
-		return new AcceptsResult($type->isUppercaseString(), []);
+		return new AcceptsResult($isUppercaseString, []);
 	}
 
 	public function isSuperTypeOf(Type $type): IsSuperTypeOfResult
diff --git a/src/Type/Accessory/NonEmptyArrayType.php b/src/Type/Accessory/NonEmptyArrayType.php
index 3015e948ce..d06699b90d 100644
--- a/src/Type/Accessory/NonEmptyArrayType.php
+++ b/src/Type/Accessory/NonEmptyArrayType.php
@@ -76,14 +76,19 @@ public function getConstantStrings(): array
 
 	public function accepts(Type $type, bool $strictTypes): AcceptsResult
 	{
+		$isArray = $type->isArray();
+		$isIterableAtLeastOnce = $type->isIterableAtLeastOnce();
+		$isNonEmptyArray = $isArray->and($isIterableAtLeastOnce);
+
+		if ($isNonEmptyArray->yes()) {
+			return AcceptsResult::createYes();
+		}
+
 		if ($type instanceof CompoundType) {
 			return $type->isAcceptedBy($this, $strictTypes);
 		}
 
-		$isArray = $type->isArray();
-		$isIterableAtLeastOnce = $type->isIterableAtLeastOnce();
-
-		return new AcceptsResult($isArray->and($isIterableAtLeastOnce), []);
+		return new AcceptsResult($isNonEmptyArray, []);
 	}
 
 	public function isSuperTypeOf(Type $type): IsSuperTypeOfResult
diff --git a/tests/PHPStan/Rules/Functions/ClosureReturnTypeRuleTest.php b/tests/PHPStan/Rules/Functions/ClosureReturnTypeRuleTest.php
index 38d4ec65d8..3e02085923 100644
--- a/tests/PHPStan/Rules/Functions/ClosureReturnTypeRuleTest.php
+++ b/tests/PHPStan/Rules/Functions/ClosureReturnTypeRuleTest.php
@@ -133,4 +133,9 @@ public function testBugFunctionMethodConstants(): void
 		$this->analyse([__DIR__ . '/data/bug-anonymous-function-method-constant.php'], []);
 	}
 
+	public function testBug13964(): void
+	{
+		$this->analyse([__DIR__ . '/data/bug-13964.php'], []);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Functions/data/bug-13964.php b/tests/PHPStan/Rules/Functions/data/bug-13964.php
new file mode 100644
index 0000000000..489a1622f8
--- /dev/null
+++ b/tests/PHPStan/Rules/Functions/data/bug-13964.php
@@ -0,0 +1,17 @@
+<?php
+
+namespace Bug13964;
+
+/** @var array<string, array<mixed>> $state */
+$state = (fn()=>[])();
+
+$state = array_map(function (array $item): array {
+	if (array_key_exists('type', $item) && array_key_exists('data', $item)) {
+		return $item;
+	}
+
+	return [
+		'type' => 'hello',
+		'data' => [],
+	];
+}, $state);
diff --git a/tests/PHPStan/Type/IntersectionTypeTest.php b/tests/PHPStan/Type/IntersectionTypeTest.php
index 7318ba9c65..e3ed23eb46 100644
--- a/tests/PHPStan/Type/IntersectionTypeTest.php
+++ b/tests/PHPStan/Type/IntersectionTypeTest.php
@@ -10,6 +10,8 @@
 use PHPStan\Type\Accessory\AccessoryArrayListType;
 use PHPStan\Type\Accessory\AccessoryLowercaseStringType;
 use PHPStan\Type\Accessory\AccessoryUppercaseStringType;
+use PHPStan\Type\Accessory\HasOffsetType;
+use PHPStan\Type\Accessory\HasOffsetValueType;
 use PHPStan\Type\Accessory\HasPropertyType;
 use PHPStan\Type\Accessory\NonEmptyArrayType;
 use PHPStan\Type\Accessory\OversizedArrayType;
@@ -70,6 +72,30 @@ public static function dataAccepts(): Iterator
 			new CallableType(),
 			TrinaryLogic::createMaybe(),
 		];
+
+		yield [
+			TypeCombinator::intersect(
+				new ArrayType(new MixedType(), new MixedType()),
+				new NonEmptyArrayType(),
+			),
+			TypeCombinator::intersect(
+				new ArrayType(new MixedType(), new MixedType()),
+				new HasOffsetType(new ConstantStringType('some-key')),
+			),
+			TrinaryLogic::createYes(),
+		];
+
+		yield [
+			TypeCombinator::intersect(
+				new ArrayType(new MixedType(), new MixedType()),
+				new NonEmptyArrayType(),
+			),
+			TypeCombinator::intersect(
+				new ArrayType(new MixedType(), new MixedType()),
+				new HasOffsetValueType(new ConstantStringType('some-key'), new IntegerType()),
+			),
+			TrinaryLogic::createYes(),
+		];
 	}
 
 	#[DataProvider('dataAccepts')]