let S be Gene-Set; :: thesis: for p1, p2 being Individual of S holds crossover p1,p2,0 ,0 ,0 ,0 ,0 = p2
let p1, p2 be Individual of S; :: thesis: crossover p1,p2,0 ,0 ,0 ,0 ,0 = p2
crossover p1,p2,0 ,0 ,0 ,0 ,0 = crossover (crossover p1,p2,0 ,0 ,0 ,0 ),p2,0 by Th32;
hence crossover p1,p2,0 ,0 ,0 ,0 ,0 = p2 by Th4; :: thesis: verum