let n1, n2, n3 be Element of NAT ; :: thesis: for S being Gene-Set
for p1, p2 being Individual of S holds crossover (p1,p2,n1,n2,n3) = crossover (p1,p2,n3,n1,n2)
let S be Gene-Set; :: thesis: for p1, p2 being Individual of S holds crossover (p1,p2,n1,n2,n3) = crossover (p1,p2,n3,n1,n2)
let p1, p2 be Individual of S; :: thesis: crossover (p1,p2,n1,n2,n3) = crossover (p1,p2,n3,n1,n2)
crossover (p1,p2,n1,n2,n3) = crossover (p1,p2,n1,n3,n2) by Th25;
hence crossover (p1,p2,n1,n2,n3) = crossover (p1,p2,n3,n1,n2) by Th25; :: thesis: verum