reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem Th27:
  for n,m st m mod 2 = 0 holds (n |^ (m div 2))^2 = n |^ m
proof
  let n,m;
  assume
A1: m mod 2 = 0;
  (n |^ (m div 2))^2 = n |^ ((m div 2) + (m div 2)) by NEWTON:8
    .= n |^ ((m + m) div 2) by A1,NAT_D:19
    .= n |^ ((2*m) div 2)
    .= n |^ m;
  hence thesis;
end;
