Object key based on array values

I have array: const arr = ['foo', 'bar', 'bax'];

I want to create an object based on array entries:

const obj = {
  foo: true,
  bar: true,
  bax: false,
  fax: true, // typescript should show error here because "fax" is not in "arr"
};

How to tell typescript that all keys of obj must be inside arr?