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;
