
theorem Th1:
  for i,n being Nat, D being non empty set, d being Element of D, z
  being Tuple of n,D st i in Seg n holds (z^<*d*>)/.i=z/.i
proof
  let i,n be Nat, D be non empty set, d be Element of D, z be Tuple of n,D
  such that
A1: i in Seg n;
  len z = n by CARD_1:def 7;
  then i in dom z by A1,FINSEQ_1:def 3;
  hence thesis by FINSEQ_4:68;
end;
