
theorem
  for a,b be positive Real, n be Nat holds
  min (a|^n,b|^n) = (min (a,b))|^n
  proof
    let a,b be positive Real, n be Nat;
    per cases;
    suppose
      A1: a >= b; then
      min (a,b) = b by XXREAL_0:def 9;
      hence thesis by A1,NEWTON02:41,XXREAL_0:def 9;
    end;
    suppose
      A1: b >= a; then
      min (a,b) = a by XXREAL_0:def 9;
      hence thesis by A1,NEWTON02:41,XXREAL_0:def 9;
    end;
  end;
