theorem Th58:
  B is constant & the_value_of B = A implies B is convergent & lim
  B = A & lim_inf B = A & lim_sup B = A
proof
  assume
A1: B is constant & the_value_of B = A;
  then for n holds (superior_setsequence(B)).n = A by Th39;
  then
A2: lim_sup B = A by Th11;
  for n holds (inferior_setsequence(B)).n = A by A1,Th38;
  then lim_inf B = A by Th10;
  hence thesis by A2,KURATO_0:def 5;
end;
