let n1, n3, n2 be Element of NAT ; :: thesis: for S being Gene-Set
for p1, p2 being Individual of S holds
( crossover p1,p2,n1,n1,n3,n3 = p1 & crossover p1,p2,n1,n2,n1,n2 = p1 & crossover p1,p2,n1,n2,n2,n1 = p1 )
let S be Gene-Set; :: thesis: for p1, p2 being Individual of S holds
( crossover p1,p2,n1,n1,n3,n3 = p1 & crossover p1,p2,n1,n2,n1,n2 = p1 & crossover p1,p2,n1,n2,n2,n1 = p1 )
let p1, p2 be Individual of S; :: thesis: ( crossover p1,p2,n1,n1,n3,n3 = p1 & crossover p1,p2,n1,n2,n1,n2 = p1 & crossover p1,p2,n1,n2,n2,n1 = p1 )
crossover p1,p2,n1,n1,n3,n3 = crossover p1,p2,n3,n3 by Th38;
hence crossover p1,p2,n1,n1,n3,n3 = p1 by Th12; :: thesis: ( crossover p1,p2,n1,n2,n1,n2 = p1 & crossover p1,p2,n1,n2,n2,n1 = p1 )
crossover p1,p2,n1,n2,n1,n2 = crossover p1,p2,n2,n2 by Th38;
hence crossover p1,p2,n1,n2,n1,n2 = p1 by Th12; :: thesis: crossover p1,p2,n1,n2,n2,n1 = p1
crossover p1,p2,n1,n2,n2,n1 = crossover p1,p2,n2,n2 by Th38;
hence crossover p1,p2,n1,n2,n2,n1 = p1 by Th12; :: thesis: verum