reserve T,T1,T2 for TopSpace,
  A,B for Subset of T,
  F for Subset of T|A,
  G,G1, G2 for Subset-Family of T,
  U,W for open Subset of T|A,
  p for Point of T|A,
  n for Nat,
  I for Integer;
reserve Af for finite-ind Subset of T,
  Tf for finite-ind TopSpace;

theorem
  for A be finite Subset of T holds ind A < card A
proof
  let A be finite Subset of T;
  A in (Seq_of_ind T).(card A) by Lm1;
  then
A1: ind A<=card A-1 by Th7;
  card A-1<card A-0 by XREAL_1:15;
  hence thesis by A1,XXREAL_0:2;
end;
