
theorem PositiveRoot:
  for a being positive Real,
      n being positive Nat holds
    n-root a is positive
  proof
    let a be positive Real,
        n be positive Nat;
I1: n-root a <> 0
    proof
      assume n-root a = 0; then
      (n-root a) |^ n = 0 |^ n;
      hence thesis;
    end;
    n >= 1 + 0 by NAT_1:13;
    hence thesis by I1,POWER:7;
  end;
