theorem Th35: :: GENEALG1:35

for n1, n2, n3, n4 being Element of NAT
for S being Gene-Set
for p1, p2 being Individual of S holds
( ( n1 >= len p1 & n2 >= len p1 & n3 >= len p1 implies crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n4) ) & ( n1 >= len p1 & n2 >= len p1 & n4 >= len p1 implies crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n3) ) & ( n1 >= len p1 & n3 >= len p1 & n4 >= len p1 implies crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n2) ) & ( n2 >= len p1 & n3 >= len p1 & n4 >= len p1 implies crossover (p1,p2,n1,n2,n3,n4) = crossover (p1,p2,n1) ) )