reserve a,b,c for set;

theorem
  for X being infinite set, x0 being set holds weight DiscrWithInfin(X,
  x0) = card X
proof
  let X be infinite set;
  let x0 be set;
  set T = DiscrWithInfin(X,x0);
  consider B0 being Basis of T such that
A1: B0 = ((SmallestPartition X) \ {{x0}}) \/ {F` where F is Subset of X:
  F is finite} by Th29;
  card B0 = card X by A1,Th32;
  hence weight T c= card X by WAYBEL23:73;
  ex B being Basis of T st card B = weight T by WAYBEL23:74;
  hence thesis by Th33;
end;
