Need help with a proof

Prove for every two distinct real numbers a and b, either

(a+b/2) > a

or

(a+b/2) > b

I haven't done math proofs in years.  I remember you should quote a rule or make a logical conversion or something for each step.

1. a and b are distinct real numbers
2. a + b/2 > a is true
3. We can simplify that to b/2 > 0
4. when b = 0, 0/2 > 2 is false

1. a and b are distinct real numbers
2. a + b/2 > b is true
3. We can simplify that to a > b/2 and then to 2a > b
4. when a = 1 and b = 2, 2 > 2 is false