reserve i,j,k,n,m for Nat,
  x,y,z,y1,y2 for object, X,Y,D for set,
  p,q for XFinSequence;
reserve k1,k2 for Nat;
reserve D for non empty set,
  F,G for XFinSequence of D,
  b for BinOp of D,
  d,d1,d2 for Element of D;
reserve F for XFinSequence,
        rF,rF1,rF2 for real-valued XFinSequence,
        r for Real,
        cF,cF1,cF2 for complex-valued XFinSequence,
        c,c1,c2 for Complex;

theorem
  for D being set holds FlattenSeq <%>(D^omega) = <%>D
proof
  let D be set;
  consider g being BinOp of D^omega such that
A1: for d1,d2 being Element of D^omega holds g.(d1,d2) = d1^d2 and
A2: FlattenSeq <%>(D^omega) = g "**" <%>(D^omega) by Def10;
A3: {} is Element of D^omega by AFINSQ_1:43;
  reconsider p = {} as Element of D^omega by AFINSQ_1:43;
  now
    let a be Element of D^omega;
    thus g.({},a) = {} ^ a by A1,A3
      .= a;
    thus g.(a,{}) = a ^ {} by A1,A3
      .= a;
  end;
  then
A4: p is_a_unity_wrt g by BINOP_1:3;
  then g "**" <%>(D^omega) = the_unity_wrt g by Th71,SETWISEO:def 2;
  hence thesis by A2,A4,BINOP_1:def 8;
end;
