let n1, n2, n3, n4 be Element of NAT ; for S being Gene-Set
for p1, p2 being Individual of S holds
( crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n2,n4,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n3,n2,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n3,n4,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n4,n3,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n1,n3,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n1,n4,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n3,n1,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n3,n4,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n4,n1,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n4,n3,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n2,n1,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n2,n4,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n4,n1,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n4,n2,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n4,n2,n3,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n4,n3,n2,n1 )
let S be Gene-Set; for p1, p2 being Individual of S holds
( crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n2,n4,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n3,n2,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n3,n4,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n4,n3,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n1,n3,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n1,n4,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n3,n1,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n3,n4,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n4,n1,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n4,n3,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n2,n1,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n2,n4,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n4,n1,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n4,n2,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n4,n2,n3,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n4,n3,n2,n1 )
let p1, p2 be Individual of S; ( crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n2,n4,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n3,n2,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n3,n4,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n4,n3,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n1,n3,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n1,n4,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n3,n1,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n3,n4,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n4,n1,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n4,n3,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n2,n1,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n2,n4,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n4,n1,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n4,n2,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n4,n2,n3,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n4,n3,n2,n1 )
A1:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n2,n4,n3
proof
set q2 =
crossover p2,
p1,
n1,
n2;
set q1 =
crossover p1,
p2,
n1,
n2;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n1,n2),
(crossover p2,p1,n1,n2),
n3,
n4
.=
crossover (crossover p1,p2,n1,n2),
(crossover p2,p1,n1,n2),
n4,
n3
by Th13
.=
crossover (crossover (crossover p1,p2,n1,n2),(crossover p2,p1,n1,n2),n4),
(crossover (crossover p2,p1,n1,n2),(crossover p1,p2,n1,n2),n4),
n3
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n1,
n2,
n4,
n3
;
verum
end;
A2: crossover p1,p2,n1,n2,n3,n4 =
crossover (crossover p1,p2,n1,n3,n2),(crossover p2,p1,n1,n2,n3),n4
by Th25
.=
crossover (crossover p1,p2,n1,n3,n2),(crossover p2,p1,n1,n3,n2),n4
by Th25
;
A3:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n3,n4,n1
proof
set q2 =
crossover p2,
p1,
n2,
n3;
set q1 =
crossover p1,
p2,
n2,
n3;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n2,n1,n3),
(crossover p2,p1,n1,n2,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3,n1),
(crossover p2,p1,n1,n2,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3,n1),
(crossover p2,p1,n2,n1,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3,n1),
(crossover p2,p1,n2,n3,n1),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3),
(crossover p2,p1,n2,n3),
n1,
n4
.=
crossover (crossover p1,p2,n2,n3),
(crossover p2,p1,n2,n3),
n4,
n1
by Th13
.=
crossover (crossover p1,p2,n2,n3,n4),
(crossover p2,p1,n2,n3,n4),
n1
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n2,
n3,
n4,
n1
;
verum
end;
A4:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n4,n3,n2
proof
set q2 =
crossover p2,
p1,
n1,
n3;
set q1 =
crossover p1,
p2,
n1,
n3;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n1,n3,n2),
(crossover p2,p1,n1,n2,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n1,n3,n2),
(crossover p2,p1,n1,n3,n2),
n4
by Th25
.=
crossover (crossover p1,p2,n1,n3),
(crossover p2,p1,n1,n3),
n2,
n4
.=
crossover (crossover p1,p2,n1,n3),
(crossover p2,p1,n1,n3),
n4,
n2
by Th13
.=
crossover (crossover p1,p2,n1,n3,n4),
(crossover p2,p1,n1,n3,n4),
n2
.=
crossover (crossover p1,p2,n1,n4,n3),
(crossover p2,p1,n1,n3,n4),
n2
by Th25
.=
crossover (crossover p1,p2,n1,n4,n3),
(crossover p2,p1,n1,n4,n3),
n2
by Th25
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n1,
n4,
n3,
n2
;
verum
end;
A5:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n4,n3,n2,n1
proof
set q2 =
crossover p2,
p1,
n3,
n2;
set q1 =
crossover p1,
p2,
n3,
n2;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n3,n1,n2),
(crossover p2,p1,n1,n2,n3),
n4
by Th26
.=
crossover (crossover p1,p2,n3,n1,n2),
(crossover p2,p1,n3,n1,n2),
n4
by Th26
.=
crossover (crossover p1,p2,n3,n2,n1),
(crossover p2,p1,n3,n1,n2),
n4
by Th25
.=
crossover (crossover p1,p2,n3,n2,n1),
(crossover p2,p1,n3,n2,n1),
n4
by Th25
.=
crossover (crossover p1,p2,n3,n2),
(crossover p2,p1,n3,n2),
n1,
n4
.=
crossover (crossover p1,p2,n3,n2),
(crossover p2,p1,n3,n2),
n4,
n1
by Th13
.=
crossover (crossover p1,p2,n3,n2,n4),
(crossover p2,p1,n3,n2,n4),
n1
.=
crossover (crossover p1,p2,n4,n3,n2),
(crossover p2,p1,n3,n2,n4),
n1
by Th26
.=
crossover (crossover p1,p2,n4,n3,n2),
(crossover p2,p1,n4,n3,n2),
n1
by Th26
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n4,
n3,
n2,
n1
;
verum
end;
A6:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n1,n4,n3
proof
set q2 =
crossover p2,
p1,
n2,
n1;
set q1 =
crossover p1,
p2,
n2,
n1;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n2,n1,n3),
(crossover p2,p1,n1,n2,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n1,n3),
(crossover p2,p1,n2,n1,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n1),
(crossover p2,p1,n2,n1),
n3,
n4
.=
crossover (crossover p1,p2,n2,n1),
(crossover p2,p1,n2,n1),
n4,
n3
by Th13
.=
crossover (crossover p1,p2,n2,n1,n4),
(crossover p2,p1,n2,n1,n4),
n3
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n2,
n1,
n4,
n3
;
verum
end;
A7:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n4,n2,n3,n1
proof
set q2 =
crossover p2,
p1,
n2,
n3;
set q1 =
crossover p1,
p2,
n2,
n3;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n2,n1,n3),
(crossover p2,p1,n1,n2,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n1,n3),
(crossover p2,p1,n2,n1,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3,n1),
(crossover p2,p1,n2,n1,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3,n1),
(crossover p2,p1,n2,n3,n1),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3),
(crossover p2,p1,n2,n3),
n1,
n4
.=
crossover (crossover p1,p2,n2,n3),
(crossover p2,p1,n2,n3),
n4,
n1
by Th13
.=
crossover (crossover p1,p2,n2,n3,n4),
(crossover p2,p1,n2,n3,n4),
n1
.=
crossover (crossover p1,p2,n4,n2,n3),
(crossover p2,p1,n2,n3,n4),
n1
by Th26
.=
crossover (crossover p1,p2,n4,n2,n3),
(crossover p2,p1,n4,n2,n3),
n1
by Th26
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n4,
n2,
n3,
n1
;
verum
end;
A8:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n3,n4,n2
proof
set q2 =
crossover p2,
p1,
n1,
n3;
set q1 =
crossover p1,
p2,
n1,
n3;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n1,n3,n2),
(crossover p2,p1,n1,n2,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n1,n3,n2),
(crossover p2,p1,n1,n3,n2),
n4
by Th25
.=
crossover (crossover p1,p2,n1,n3),
(crossover p2,p1,n1,n3),
n2,
n4
.=
crossover (crossover p1,p2,n1,n3),
(crossover p2,p1,n1,n3),
n4,
n2
by Th13
.=
crossover (crossover (crossover p1,p2,n1,n3),(crossover p2,p1,n1,n3),n4),
(crossover (crossover p2,p1,n1,n3),(crossover p1,p2,n1,n3),n4),
n2
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n1,
n3,
n4,
n2
;
verum
end;
A9:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n2,n4,n1
proof
set q2 =
crossover p2,
p1,
n3,
n2;
set q1 =
crossover p1,
p2,
n3,
n2;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n3,n1,n2),
(crossover p2,p1,n1,n2,n3),
n4
by Th26
.=
crossover (crossover p1,p2,n3,n1,n2),
(crossover p2,p1,n3,n1,n2),
n4
by Th26
.=
crossover (crossover p1,p2,n3,n2,n1),
(crossover p2,p1,n3,n1,n2),
n4
by Th25
.=
crossover (crossover p1,p2,n3,n2,n1),
(crossover p2,p1,n3,n2,n1),
n4
by Th25
.=
crossover (crossover p1,p2,n3,n2),
(crossover p2,p1,n3,n2),
n1,
n4
.=
crossover (crossover p1,p2,n3,n2),
(crossover p2,p1,n3,n2),
n4,
n1
by Th13
.=
crossover (crossover p1,p2,n3,n2,n4),
(crossover p2,p1,n3,n2,n4),
n1
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n3,
n2,
n4,
n1
;
verum
end;
A10:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n4,n1,n3
proof
set q2 =
crossover p2,
p1,
n2,
n1;
set q1 =
crossover p1,
p2,
n2,
n1;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n2,n1,n3),
(crossover p2,p1,n1,n2,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n1,n3),
(crossover p2,p1,n2,n1,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n1),
(crossover p2,p1,n2,n1),
n3,
n4
.=
crossover (crossover p1,p2,n2,n1),
(crossover p2,p1,n2,n1),
n4,
n3
by Th13
.=
crossover (crossover p1,p2,n2,n1,n4),
(crossover p2,p1,n2,n1,n4),
n3
.=
crossover (crossover p1,p2,n2,n4,n1),
(crossover p2,p1,n2,n1,n4),
n3
by Th25
.=
crossover (crossover p1,p2,n2,n4,n1),
(crossover p2,p1,n2,n4,n1),
n3
by Th25
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n2,
n4,
n1,
n3
;
verum
end;
A11:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n4,n2,n1
proof
set q2 =
crossover p2,
p1,
n3,
n2;
set q1 =
crossover p1,
p2,
n3,
n2;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n3,n1,n2),
(crossover p2,p1,n1,n2,n3),
n4
by Th26
.=
crossover (crossover p1,p2,n3,n1,n2),
(crossover p2,p1,n3,n1,n2),
n4
by Th26
.=
crossover (crossover p1,p2,n3,n2,n1),
(crossover p2,p1,n3,n1,n2),
n4
by Th25
.=
crossover (crossover p1,p2,n3,n2,n1),
(crossover p2,p1,n3,n2,n1),
n4
by Th25
.=
crossover (crossover p1,p2,n3,n2),
(crossover p2,p1,n3,n2),
n1,
n4
.=
crossover (crossover p1,p2,n3,n2),
(crossover p2,p1,n3,n2),
n4,
n1
by Th13
.=
crossover (crossover p1,p2,n3,n2,n4),
(crossover p2,p1,n3,n2,n4),
n1
.=
crossover (crossover p1,p2,n3,n4,n2),
(crossover p2,p1,n3,n2,n4),
n1
by Th25
.=
crossover (crossover p1,p2,n3,n4,n2),
(crossover p2,p1,n3,n4,n2),
n1
by Th25
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n3,
n4,
n2,
n1
;
verum
end;
A12: crossover p1,p2,n1,n2,n3,n4 =
crossover (crossover p1,p2,n3,n1,n2),(crossover p2,p1,n1,n2,n3),n4
by Th26
.=
crossover (crossover p1,p2,n3,n1,n2),(crossover p2,p1,n3,n1,n2),n4
by Th26
.=
crossover (crossover p1,p2,n3,n2,n1),(crossover p2,p1,n3,n1,n2),n4
by Th25
.=
crossover (crossover p1,p2,n3,n2,n1),(crossover p2,p1,n3,n2,n1),n4
by Th25
;
A13:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n4,n1,n2
proof
set q2 =
crossover p2,
p1,
n3,
n1;
set q1 =
crossover p1,
p2,
n3,
n1;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n3,n1,n2),
(crossover p2,p1,n1,n2,n3),
n4
by Th26
.=
crossover (crossover p1,p2,n3,n1,n2),
(crossover p2,p1,n3,n1,n2),
n4
by Th26
.=
crossover (crossover p1,p2,n3,n1),
(crossover p2,p1,n3,n1),
n2,
n4
.=
crossover (crossover p1,p2,n3,n1),
(crossover p2,p1,n3,n1),
n4,
n2
by Th13
.=
crossover (crossover p1,p2,n3,n1,n4),
(crossover p2,p1,n3,n1,n4),
n2
.=
crossover (crossover p1,p2,n3,n4,n1),
(crossover p2,p1,n3,n1,n4),
n2
by Th25
.=
crossover (crossover p1,p2,n3,n4,n1),
(crossover p2,p1,n3,n4,n1),
n2
by Th25
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n3,
n4,
n1,
n2
;
verum
end;
A14:
crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n4,n3,n1
proof
set q2 =
crossover p2,
p1,
n2,
n3;
set q1 =
crossover p1,
p2,
n2,
n3;
crossover p1,
p2,
n1,
n2,
n3,
n4 =
crossover (crossover p1,p2,n2,n1,n3),
(crossover p2,p1,n1,n2,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3,n1),
(crossover p2,p1,n1,n2,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3,n1),
(crossover p2,p1,n2,n1,n3),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3,n1),
(crossover p2,p1,n2,n3,n1),
n4
by Th25
.=
crossover (crossover p1,p2,n2,n3),
(crossover p2,p1,n2,n3),
n1,
n4
.=
crossover (crossover p1,p2,n2,n3),
(crossover p2,p1,n2,n3),
n4,
n1
by Th13
.=
crossover (crossover p1,p2,n2,n3,n4),
(crossover p2,p1,n2,n3,n4),
n1
.=
crossover (crossover p1,p2,n2,n4,n3),
(crossover p2,p1,n2,n3,n4),
n1
by Th25
.=
crossover (crossover p1,p2,n2,n4,n3),
(crossover p2,p1,n2,n4,n3),
n1
by Th25
;
hence
crossover p1,
p2,
n1,
n2,
n3,
n4 = crossover p1,
p2,
n2,
n4,
n3,
n1
;
verum
end;
A15: crossover p1,p2,n1,n2,n3,n4 =
crossover (crossover p1,p2,n2,n1,n3),(crossover p2,p1,n1,n2,n3),n4
by Th25
.=
crossover (crossover p1,p2,n2,n1,n3),(crossover p2,p1,n2,n1,n3),n4
by Th25
;
crossover p1,p2,n1,n2,n3,n4 =
crossover (crossover p1,p2,n2,n1,n3),(crossover p2,p1,n1,n2,n3),n4
by Th25
.=
crossover (crossover p1,p2,n2,n1,n3),(crossover p2,p1,n2,n1,n3),n4
by Th25
.=
crossover (crossover p1,p2,n2,n3,n1),(crossover p2,p1,n2,n1,n3),n4
by Th25
.=
crossover (crossover p1,p2,n2,n3,n1),(crossover p2,p1,n2,n3,n1),n4
by Th25
;
hence
( crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n2,n4,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n3,n2,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n3,n4,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n1,n4,n3,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n1,n3,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n1,n4,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n3,n1,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n3,n4,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n4,n1,n3 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n2,n4,n3,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n2,n1,n4 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n2,n4,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n4,n1,n2 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n3,n4,n2,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n4,n2,n3,n1 & crossover p1,p2,n1,n2,n3,n4 = crossover p1,p2,n4,n3,n2,n1 )
by A2, A15, A1, A8, A4, A6, A3, A10, A14, A12, A9, A13, A11, A7, A5; verum