
theorem Th50:
  for A be finite set, B be non empty set,
      f be B-valued total A-defined Function
  holds f * canFS(A) is FinSequence of B
  proof
    let A be finite set, B be non empty set,
        f be B-valued total A-defined Function;
    A1: rng(f * canFS(A)) c= B;
    A = dom f & rng canFS(A) = A by FUNCT_2:def 3,PARTFUN1:def 2; then
    dom(f * canFS(A)) = dom canFS(A) by RELAT_1:27; then
    dom(f * canFS(A)) = Seg len canFS(A) by FINSEQ_1:def 3; then
    f * canFS(A) is FinSequence by FINSEQ_1:def 2;
    hence thesis by A1,FINSEQ_1:def 4;
  end;
