theorem Th37: :: GENEALG1:37

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,n2,n3,n4) = crossover (p1,p2,n1,n2,n4,n3) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n1,n3,n2,n4) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n1,n3,n4,n2) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n1,n4,n3,n2) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n2,n1,n3,n4) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n2,n1,n4,n3) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n2,n3,n1,n4) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n2,n3,n4,n1) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n2,n4,n1,n3) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n2,n4,n3,n1) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n3,n2,n1,n4) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n3,n2,n4,n1) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n3,n4,n1,n2) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n3,n4,n2,n1) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n4,n2,n3,n1) & crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n4,n3,n2,n1) )