theorem Th31: :: GENEALG1:31
for n1, n2, n3, n4 being Element of NAT
for S being Gene-Set
for p1, p2 being Individual of S holds
( crossover (p1,p2,n1,0,0,0) = crossover (p2,p1,n1) & crossover (p1,p2,0,n2,0,0) = crossover (p2,p1,n2) & crossover (p1,p2,0,0,n3,0) = crossover (p2,p1,n3) & crossover (p1,p2,0,0,0,n4) = crossover (p2,p1,n4) )