let S be Gene-Set; :: thesis: for p1, p2 being Individual of S holds crossover p1,p2,0 = p2
let p1, p2 be Individual of S; :: thesis: crossover p1,p2,0 = p2
crossover p1,p2,0 = p2 /^ 0 by FINSEQ_1:47
.= p2 by FINSEQ_5:31 ;
hence crossover p1,p2,0 = p2 ; :: thesis: verum