reserve r,r1,r2,g,g1,g2,x0,t for Real;
reserve n,k,m for Element of NAT;
reserve seq for Real_Sequence;
reserve f,f1,f2 for PartFunc of REAL,REAL;

theorem Th32:
  f is_convergent_in x0 implies -f is_convergent_in x0 & lim(-f,x0
  )=-(lim(f,x0))
proof
  assume
A1: f is_convergent_in x0;
  thus -f is_convergent_in x0 by A1,Th31;
  thus lim(-f,x0)=(-1)*(lim(f,x0)) by A1,Th31
    .=-(lim(f,x0));
end;
