reserve i,n,m,k,x,y for Nat,
  i1 for Integer;

theorem Th1:
  2 <= k implies 2 < Radix(k)
proof
  defpred P[Nat] means 2 < Radix($1);
A1: for kk be Nat st kk >= 2 & P[kk] holds P[kk + 1]
  proof
    let kk be Nat;
    assume that
    2 <= kk and
A2: 2 < Radix(kk);
A3: Radix(kk + 1) = 2 to_power (1) * 2 to_power (kk) by POWER:27
      .= 2 * Radix(kk) by POWER:25;
    Radix(kk) > 1 by A2,XXREAL_0:2;
    hence thesis by A3,XREAL_1:155;
  end;
  Radix(2) = 2 to_power (1+1) .= 2 to_power 1 * 2 to_power 1 by POWER:27
    .= 2 * (2 to_power 1) by POWER:25
    .= 2 * 2 by POWER:25
    .= 4;
  then
A4: P[2];
  for k be Nat holds 2 <= k implies P[k] from NAT_1:sch 8(A4,A1);
  hence thesis;
end;
