match with int() and bool()

Question

With Python 3.10.2, consider this code snippet.

def print_type(v):
    match v:
        case int() as v:
            s = f"int {v}"
        case bool() as v:
            s = f"bool {v}"
        case _:
            s = "other"
    print(s)

Try it with 's = False' and it will print 'bool False' as expected. Now reverse the bool() and int() cases and the result will now be 'int False'. Not exactly what I expected.

Is it a bug? If so, I'll post on the Python forum.

EDIT

Based on trincot's answer, here is a version of the code that has the expected behavior.

def print_type(v):
    match v:
        case int() as v:
            if isinstance(v, bool):
                s = f"bool {v}"
            else:
                s = f"int {v}"
        case _:
            s = "other"
    print(s)

Answer 1

No, this is not a bug. bool is a subclass of int, and so every boolean is also an integer.

print(isinstance(True, int))  # True