reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;
reserve D for set,
  f for FinSequence of D;

theorem Th83:
  for p be FinSequence for i be Nat st i < len p
  holds p|(i+1) = p|i ^ <*p.(i+1)*>
proof
  let p be FinSequence;
  let i be Nat;
  assume i < len p;
  then
A1: i+1 <= len p by NAT_1:13;
  1 <= i+1 by NAT_1:11;
  then
  i+1 in dom p by A1,FINSEQ_3:25;
  hence thesis by Th10;
end;
