theorem :: GROUP_24:114

for n being non zero even Nat
for k being Nat st n = 2 * k holds
for g1 being Element of (INT.Group n) st g1 = 1 holds
for x being Element of (Dihedral_group n) st x = <*g1,(1_ (INT.Group 2))*> holds
(x |^ k) |^ 2 = 1_ (Dihedral_group n)