reserve X for set;
reserve UN for Universe;

theorem Th69:
  for UN being Universe
  for X being set st X in UN holds
  for s being FinSequence of X holds s in UN
  proof
    let UN be Universe;
    let X be set;
    assume
A1: X in UN;
    let s be FinSequence of X;
    consider n be Nat such that
A2: dom s = Seg n by FINSEQ_1:def 2;
    rng s c= X;
    then
A3: s is Function of dom s,X by FUNCT_2:2;
    Seg n in UN by Th57;
    then [: Seg n, X:] in UN by A1,CLASSES2:61;
    hence thesis by A3,A2,Th13;
  end;
