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 Th13:
  for k,n being Nat holds
  (n <= k & 1 <= n & n <= len f implies (con f)/.n = (con (f|k))/.n)
  proof
    let k,n be Nat;
    assume that
A1: n <= k and
A2: 1 <= n and
A3: n <= len f;
A4: n <= len con f by A2,A3,Def2;
    per cases;
    suppose
      k <= len f;
      then A5: n <= len (f|k) by FINSEQ_1:59,A1;
      then A6: len con (f|k) = len (f|k) by A2,Def2;
      thus (con f)/.n = (con f).n by FINSEQ_4:15,A2,A4
      .= (con (f|k)).n by Th12,A1
      .= (con (f|k))/.n by FINSEQ_4:15,A2, A6,A5;
    end;
    suppose
      k > len f;
      hence (con f)/.n = (con (f|k))/.n by FINSEQ_1:58;
    end;
  end;
