let n1, n2, n3, n4, n5 be Element of NAT ; :: thesis: for S being Gene-Set
for p1, p2 being Individual of S st n1 >= len p1 & n2 >= len p1 & n3 >= len p1 & n4 >= len p1 & n5 >= len p1 holds
crossover p1,p2,n1,n2,n3,n4,n5 = p1
let S be Gene-Set; :: thesis: for p1, p2 being Individual of S st n1 >= len p1 & n2 >= len p1 & n3 >= len p1 & n4 >= len p1 & n5 >= len p1 holds
crossover p1,p2,n1,n2,n3,n4,n5 = p1
let p1, p2 be Individual of S; :: thesis: ( n1 >= len p1 & n2 >= len p1 & n3 >= len p1 & n4 >= len p1 & n5 >= len p1 implies crossover p1,p2,n1,n2,n3,n4,n5 = p1 )
assume A1: ( n1 >= len p1 & n2 >= len p1 & n3 >= len p1 & n4 >= len p1 & n5 >= len p1 ) ; :: thesis: crossover p1,p2,n1,n2,n3,n4,n5 = p1
then crossover p1,p2,n1,n2,n3,n4,n5 = crossover p1,(crossover p2,p1,n1,n2,n3,n4),n5 by Th36;
hence crossover p1,p2,n1,n2,n3,n4,n5 = p1 by A1, Th5; :: thesis: verum