reserve
  A,B,X for set,
  S for SigmaField of X;
reserve C for C_Measure of X;

theorem Th11:
  for N being sequence of S holds for A being Element of S
holds ex F being sequence of S st for n being Element of NAT holds F.n = A
  /\ N.n
proof
  let N be sequence of S;
  let A be Element of S;
  defpred P[object,object] means ($1 in NAT implies $2 = A /\ N.$1);
A1: for x being object st x in NAT ex y being object st y in S & P[x,y]
  proof
    let x be object;
    assume x in NAT;
    then reconsider x as Element of NAT;
    consider y being set such that
A2: y = A /\ N.x;
    take y;
    thus thesis by A2;
  end;
  ex F being sequence of S st for x being object st x in NAT holds P[x,F.
  x] from FUNCT_2:sch 1(A1);
  then consider F being sequence of S such that
A3: for x being object st x in NAT holds P[x,F.x];
  take F;
  thus thesis by A3;
end;
