
theorem Th2:
  for D being set holds FlattenSeq <*>(D*) = <*>D
proof
  let D be set;
  consider g being BinOp of D* such that
A1: for d1,d2 being Element of D* holds g.(d1,d2) = d1^d2 and
A2: FlattenSeq <*>(D*) = g "**" <*>(D*) by Def1;
A3: {} is Element of D* by FINSEQ_1:49;
  reconsider p = {} as Element of D* by FINSEQ_1:49;
  now
    let a be Element of D*;
    thus g.({},a) = {} ^ a by A1,A3
      .= a by FINSEQ_1:34;
    thus g.(a,{}) = a ^ {} by A1,A3
      .= a by FINSEQ_1:34;
  end;
  then
A4: p is_a_unity_wrt g by BINOP_1:3;
  then g "**" <*>(D*) = the_unity_wrt g by FINSOP_1:10,SETWISEO:def 2;
  hence thesis by A2,A4,BINOP_1:def 8;
end;
