solar array tie-in to sub panel

I am installing a 6.7kw solar edge system with optimizers on my barn.  i am using the upgraded inverter which is a se7600 and will feed a 40 amp breaker in my barn sub panel (this allows me some expanding of system in future).  I will derated my exsisting 100 amp barn sub panel to  60 amps (60A + 40A = 100amps less than 120A max.). But, The question is: What size breaker can i use at my main 200amp main panel (#2wire) at my house to feed/backfeed barn sub panel? The solar company tells me that 40A only as the main feed/backfeed to barn from the main panel, but i was thinking 60A is about the smallest i need for power to the barn to work at night.  The 40 amp solar Array is still 40A and can not backfeed 60 amps back to the main panel. Correct?  So i should meet the 120% rule, and still allow max 60amp feed to barn at night.  I need some help[ here please. Please advise.

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