theorem Th24: :: NOMIN_4:25

for V, A being set
for a, b being Element of V
for x, y being object
for x0, y0 being Nat st not V is empty & A is_without_nonatomicND_wrt V & a <> b & a <> y & A is complex-containing & ( for d being TypeSCNominativeData of V,A holds a is_complex_on d ) & ( for d being TypeSCNominativeData of V,A holds b is_complex_on d ) holds
<*(valid_gcd_input (V,A,x,y,x0,y0)),(gcd_main_part (V,A,a,b,x,y)),(PP_and ((Equality (A,a,b)),(gcd_inv (V,A,a,b,x0,y0))))*> is SFHT of (ND (V,A))