diff --git a/src/Type/IntersectionType.php b/src/Type/IntersectionType.php
index 72fecc7de6..32c194660b 100644
--- a/src/Type/IntersectionType.php
+++ b/src/Type/IntersectionType.php
@@ -756,7 +756,14 @@ public function setOffsetValueType(?Type $offsetType, Type $valueType, bool $uni
 				);
 			});
 		}
-		return $this->intersectTypes(static fn (Type $type): Type => $type->setOffsetValueType($offsetType, $valueType, $unionValues));
+
+		$result = $this->intersectTypes(static fn (Type $type): Type => $type->setOffsetValueType($offsetType, $valueType, $unionValues));
+
+		if ($offsetType !== null && $this->isList()->yes() && $this->isIterableAtLeastOnce()->yes() && (new ConstantIntegerType(1))->isSuperTypeOf($offsetType)->yes()) {
+			$result = TypeCombinator::intersect($result, new AccessoryArrayListType());
+		}
+
+		return $result;
 	}
 
 	public function setExistingOffsetValueType(Type $offsetType, Type $valueType): Type
diff --git a/tests/PHPStan/Rules/Properties/TypesAssignedToPropertiesRuleTest.php b/tests/PHPStan/Rules/Properties/TypesAssignedToPropertiesRuleTest.php
index ff9f5be5ae..e140807b35 100644
--- a/tests/PHPStan/Rules/Properties/TypesAssignedToPropertiesRuleTest.php
+++ b/tests/PHPStan/Rules/Properties/TypesAssignedToPropertiesRuleTest.php
@@ -692,4 +692,10 @@ public function testBug11617(): void
 		]);
 	}
 
+	public function testBug12131(): void
+	{
+		$this->checkExplicitMixed = true;
+		$this->analyse([__DIR__ . '/data/bug-12131.php'], []);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Properties/data/bug-12131.php b/tests/PHPStan/Rules/Properties/data/bug-12131.php
new file mode 100755
index 0000000000..1442cce55d
--- /dev/null
+++ b/tests/PHPStan/Rules/Properties/data/bug-12131.php
@@ -0,0 +1,29 @@
+<?php declare(strict_types = 1); // lint >= 7.4
+
+namespace Bug12131;
+
+class Test
+{
+	/**
+	 * @var non-empty-list<int>
+	 */
+	public array $array;
+
+	public function __construct()
+	{
+		$this->array = array_fill(0, 10, 1);
+	}
+
+	public function setAtZero(): void
+	{
+		$this->array[0] = 1;
+	}
+
+	public function setAtOne(): void
+	{
+		$this->array[1] = 1;
+	}
+}
+
+$a = new Test();
+$a->setAtOne();