theorem
  f1 is convergent_in-infty & f2 is convergent_in-infty & (for r ex g st
g<r & g in dom(f1-f2)) implies f1-f2 is convergent_in-infty & lim_in-infty(f1-
  f2)=(lim_in-infty f1)-(lim_in-infty f2)
proof
  assume that
A1: f1 is convergent_in-infty and
A2: f2 is convergent_in-infty and
A3: for r ex g st g<r & g in dom(f1-f2);
A4: -f2 is convergent_in-infty by A2,Th90;
  hence f1-f2 is convergent_in-infty by A1,A3,Th91;
  lim_in-infty(-f2)=-(lim_in-infty f2) by A2,Th90;
  hence lim_in-infty(f1-f2)=lim_in-infty f1+-lim_in-infty f2 by A1,A3,A4,Th91
    .=lim_in-infty f1-lim_in-infty f2;
end;
