reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem POW1:
  for a,b be non negative Real, n be positive Nat holds
    a|^n = b|^n iff a = b
  proof
    let a,b be non negative Real, n be positive Nat;
    (a > b implies a|^n > b|^n) &
    (a < b implies a|^n < b|^n) by NEWTON02:40;
    hence thesis by XXREAL_0:1;
  end;
