theorem :: NOMIN_4:28

for V, A being set
for a, b, z 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_program (V,A,a,b,x,y,z)),(valid_gcd_output (V,A,z,x0,y0))*> is SFHT of (ND (V,A))