reserve a,b,c for set;

theorem Th14:
  for T being discrete non empty TopStruct holds weight T = card
  the carrier of T
proof
  let T be discrete non empty TopStruct;
  set M = the set of all card C where C is Basis of T;
  reconsider B0 = SmallestPartition the carrier of T as Basis of T by Th13;
A1: card B0 in M;
A2: card B0 = card the carrier of T by Th12;
  weight T = meet M by WAYBEL23:def 5;
  hence weight T c= card the carrier of T by A2,A1,SETFAM_1:3;
  ex B being Basis of T st card B = weight T by WAYBEL23:74;
  hence card the carrier of T c= weight T by A2,Th13,CARD_1:11;
end;
