
theorem LMXFIN15:
  for k be Nat,
  c be XFinSequence of REAL holds
  ex d be XFinSequence of REAL st len d = len c &
  for i be Nat st i in dom d holds d.i = |. c.i .|
  proof
    let k be Nat,
    c be XFinSequence of REAL;
    deffunc F(Nat) = In(|. c.$1 .|,REAL);
    consider d being XFinSequence of REAL such that
    A1: len d = len c &
    for j be Nat st j in len c holds d.j = F(j) from AFINSQ_2:sch 1;
    take d;
    thus len d = len c by A1;
    let i be Nat;
    assume i in dom d;
    then d.i = In(|. c.i .|,REAL) by A1;
    hence d.i = |. c.i .|;
  end;
