let n2, n3, n1 be Element of NAT ; :: thesis: for S being Gene-Set
for p1, p2 being Individual of S st n2 >= len p1 & n3 >= len p1 holds
crossover p1,p2,n1,n2,n3 = crossover p1,p2,n1
let S be Gene-Set; :: thesis: for p1, p2 being Individual of S st n2 >= len p1 & n3 >= len p1 holds
crossover p1,p2,n1,n2,n3 = crossover p1,p2,n1
let p1, p2 be Individual of S; :: thesis: ( n2 >= len p1 & n3 >= len p1 implies crossover p1,p2,n1,n2,n3 = crossover p1,p2,n1 )
assume that
A1: n2 >= len p1 and
A2: n3 >= len p1 ; :: thesis: crossover p1,p2,n1,n2,n3 = crossover p1,p2,n1
crossover p1,p2,n1,n2,n3 = crossover p1,p2,n1,n3 by A1, Th19;
hence crossover p1,p2,n1,n2,n3 = crossover p1,p2,n1 by A2, Th10; :: thesis: verum