Is Type Irrelevant As Long As Value Is Within Boundaries Of Type Of Switch Expression

If you have final int i = 1;
short s = 1;
switch(s) {
case i: System.out.println(i);
}

it runs fine. Note that the switch expression is of type short (2 bytes) and the case constant is of type int (4 bytes).My question is: Is the type irrelevant as long as the value is within the boundaries of the type of the switch expression?I have the feeling that this is true since:

byte b = 127;
final int i = 127;
switch(b) {
case i: System.out.println(i);
}

This runs fine again, but if I change the literal assigned to i to 128, which is out of range for type byte, then the compiler complains.Is it true that in the first example the short variable and in the second example the byte variable (the switch expressions) are first implicitly converted to an int and then compared with the case constants?