theorem Th81:
  f is convergent_in+infty implies -f is convergent_in+infty &
  lim_in+infty(-f)=-(lim_in+infty f)
proof
  assume
A1: f is convergent_in+infty;
  thus -f is convergent_in+infty by A1,Th80;
  thus lim_in+infty (-f)=(-jj)*(lim_in+infty f) by A1,Th80
    .=-(lim_in+infty f);
end;
