theorem Th8: :: NOMIN_6:8

for V, A being set
for loc being b₁ -valued Function
for val being Function
for n0 being Nat
for b0 being Complex st not V is empty & A is complex-containing & A is_without_nonatomicND_wrt V & loc /. 1,loc /. 2,loc /. 3,loc /. 4,loc /. 5 are_mutually_distinct & loc,val are_compatible_wrt_5_locs holds
<*(valid_power_input (V,A,val,b0,n0)),(power_main_part (A,loc,val)),(PP_and ((Equality (A,(loc /. 1),(loc /. 4))),(power_inv (A,loc,b0,n0))))*> is SFHT of (ND (V,A))