reserve A,B,p,q,r,s for Element of LTLB_WFF,
  i,j,k,n for Element of NAT,
  X for Subset of LTLB_WFF,
  f,f1 for FinSequence of LTLB_WFF,
  g for Function of LTLB_WFF,BOOLEAN;

theorem Th3:
  for f,g be FinSequence st rng f = rng g holds (len f = 0 iff len g = 0)
  proof
    let f,g be FinSequence;
    assume
A1: rng f = rng g;
    hereby
      assume
      len f = 0;
      then f = {};
      then g = {} by RELAT_1:38,A1 ,RELAT_1:41;
      hence len g = 0;
    end;
    assume
    len g = 0;
    then g = {};
    then f = {} by RELAT_1:38,A1 ,RELAT_1:41;
    hence len f = 0;
  end;
