theorem Th64:
  B is non-ascending implies B is convergent & lim B = Intersection B
proof
  assume
A1: B is non-ascending;
  then lim_sup B = Intersection B & lim_inf B = Intersection B by Th49,Th53;
  hence B is convergent by KURATO_0:def 5;
  thus thesis by A1,Th49;
end;
