I'm a bit confused here.
The FMC will automaticaly select a corresponding climb thrust which should be the same or higher than the reduced take off thrust,
That is not as I understand it. I have always seen a thrust REDUCTION upon selection (automatically or otherwise) of climb thrust. Mr Boeing's publication for the 737 has this to say on the matter:
The FMC automatically selects the highest climb thrust available (CLB, CLB-1, CLB-2) which would not result in a thrust lever push, when the aircraft transitions from takeoff to climb.
Please explain in language suitable for someone who is halfway down his second bottle of red .. (days off!!) ..
Thanks