reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;
reserve s for Element of D*;

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;
