reserve i,j,n,n1,n2,m,k,u for Nat,
        r,r1,r2 for Real,
        x,y for Integer,
        a,b for non trivial Nat;

theorem Th23:
  x >=0 implies sgn(x)*Py(a,|.x.|) = Py(a,|.x.|)
proof
  assume x>=0;
  then x=0 or x >0;
  then sgn(x) =1 or (sgn(x)=0 & x=0) by ABSVALUE:def 2;
  hence thesis by Th6;
end;
