reserve x,y,z for Real,
  a,b,c,d,e,f,g,h for Nat,
  k,l,m,n,m1,n1,m2,n2 for Integer,
  q for Rational;

theorem Th2:
  for a being Nat holds (-x)|^(2*a)=x|^(2*a) & (-x)|^(2*a+1)=-(x|^( 2*a+1))
proof
  let a be Nat;
A1: (-x)|^(2*a)=((-x)|^2)|^a by NEWTON:9
    .=(x|^2)|^a by Th1
    .=x|^(2*a) by NEWTON:9;
  (-x)|^(2*a+1)=((-x)|^(2*a))*(-x) by NEWTON:6
    .=-(x|^(2*a))*x by A1
    .=-(x|^(2*a+1)) by NEWTON:6;
  hence thesis by A1;
end;
