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 n in dom f implies (VAL g).((con f)/.len con f) =
  (VAL g).((con (f|(n -' 1)))/.(len con (f|(n -' 1)))) '&' (VAL g).(f/.n) '&'
  (VAL g).((con (f/^n))/.(len con (f/^n)))
  proof
    set v = VAL g;
    assume n in dom f;
    then A1: 1 <= n & n <=len f by FINSEQ_3:25;
    then f = (f|(n -' 1))^<*(f.n)*>^(f/^ n) by FINSEQ_5:84
    .= (f|(n -' 1))^<*(f/.n)*>^(f/^ n) by FINSEQ_4:15,A1;
    hence v.kon(f)=v.kon((f|(n -' 1))^<*(f/.n)*>) '&' v.kon(f/^ n) by Th17
    .= v.kon(f|(n -' 1)) '&' v.kon(<*(f/.n)*>) '&' v.kon(f/^ n) by Th17
    .= v.kon(f|(n-'1)) '&' v.(f/.n) '&' v.kon(f/^n) by Th11;
  end;
