 reserve Exx for Real;

theorem ThA:
  for AA being SetSequence of REAL holds
   ex A being SetSequence of REAL st
  for n being Nat holds A.n=(Partial_Union AA).n
 proof
  let AA be SetSequence of REAL;
  deffunc U(Nat) = (Partial_Union AA).$1;
  consider f being SetSequence of REAL such that
A1: for d be Element of NAT holds f.d = U(d) from FUNCT_2:sch 4;
  take f;
  let n be Nat;
  n in NAT by ORDINAL1:def 12;
  hence thesis by A1;
 end;
