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

theorem Th44:
  f is_left_convergent_in x0 implies -f is_left_convergent_in x0 &
  lim_left(-f,x0)=-(lim_left(f,x0))
proof
  assume
A1: f is_left_convergent_in x0;
  thus -f is_left_convergent_in x0 by A1,Th43;
  thus lim_left(-f,x0)=(-1)*(lim_left(f,x0)) by A1,Th43
    .=-(lim_left(f,x0));
end;
