
theorem Lmkdf:
  for a be Complex, f be FinSequence, k be Nat st k in dom f holds
    ((len f) |-> a).k = a
  proof
    let a be Complex;
    let f be FinSequence;
    let k be Nat;
    assume k in dom f; then
    (len f) >= k >= 1 by FINSEQ_3:25; then
    k in Seg (len f);
    hence thesis by FINSEQ_2:57;
  end;
