To spell it out, using a 10000# thrust engine for example:
At zero TAS, THP = 0
At 375 MPH (i.e. 550 fps) TAS, THP = 10000
At 750 MPH (i.e. 1100 fps) TAS, THP = 20000
...and so on. As you see, the propulsive work delivered to the aeroplane increases proportional to velocity.
In real life, things aren't so tidy, simply because the engine thrust varies a bit with different inlet conditions; but if the machine were adjusted to hold constant thrust, the above would indeed apply.
HINT: Note that the above cases are based on the definition of 1 HP, namely 33000 ft-lb/min, or 550 ft-lb/sec. It helps to think of horsepower in terms of its definition!