
theorem Th2:
  for n being Nat, D being non empty set, d being Element of D, z
  being Tuple of n,D holds (z^<*d*>)/.(n+1)=d
proof
  let n be Nat, D be non empty set, d be Element of D, z be Tuple of n,D;
  len<*d*> = 1 by FINSEQ_1:39;
  then 0+1 in Seg len <*d*>;
  then
A1: 0+1 in dom <*d*> by FINSEQ_1:def 3;
  len(z) = n by CARD_1:def 7;
  hence (z^<*d*>)/.(n+1) = <*d*>/.1 by A1,FINSEQ_4:69
    .= d by FINSEQ_4:16;
end;
