theorem
  for z1,z2 being Tuple of i,D st for j being Nat st j in Seg i holds
  z1.j = z2.j holds z1 = z2
proof
  let z1,z2 be Tuple of i,D;
  len z2 = i by CARD_1:def 7;
  then
A1: dom z2 = Seg i by FINSEQ_1:def 3;
  len z1 = i by CARD_1:def 7;
  then dom z1 = Seg i by FINSEQ_1:def 3;
  hence thesis by A1;
end;
