enigmatic "name already defined" error

Please provide more information to help us understand the issue:

• Are you reporting a bug, or opening a feature request?

Bug.

• Please insert below the code you are checking with mypy,
  or a mock-up repro if the source is private. We would appreciate
  if you try to simplify your case to a minimal repro.

There are four pieces of code:

def func(x: int) -> int:
    return x + 1

def func(x):
    return x

def func(x):
    return x

def func(x: int) -> int:
    return x + 1

from test import func

def func(x: int) -> int:
    return x + 1

def func(x: int) -> int:
    return x + 1

from test import func

Whenever test is used as a module, test.py contains

def func(x):
    return x

• What is the actual behavior/output?

The first three examples emits "Name 'func' already defined" error, but not the last

• What is the behavior/output you expect?

All four should emit this error.

• What are the versions of mypy and Python you are using?

mypy 0.720+dev.dc6da54f50d5443fe46308046719043eba03c84d (master at the time of bug report)
Python 3.7.3

• What are the mypy flags you are using? (For example --strict-optional)

None.

Start by running the four inline reproductions with the reported mypy version, using test.py for the imported function. Compare the diagnostics for each import and redefinition order. Done means the behavior is consistent with the report's expectation that all four cases emit the duplicate-definition error.