"I think his question was "why de-rated thrust uses more trip fuel"?"
I think this is a very good question. Can anyone confirm that this is even true? Consider that the best specific fuel consumption (SFC), which is thrust produced per pound of fuel consumed, is not at max N1, but in a range of 93 to 97 %, depending on the engine. Ergo, one can expect less fuel consumed.
Which leads to the further thought; Does max rate of climb mean minimum fuel burned?
Hawk