theorem Th30:
  for A,D being set for p being FinSequence of A for f being
  Function of A,D holds f*p is FinSequence of D
proof
  let A,D be set;
  let p be FinSequence of A;
  let f be Function of A,D;
  per cases;
  suppose D = {};
    then f*p = <*>D;
    hence thesis;
  end;
  suppose
A1: D <> {};
A2: rng p c= A by RELAT_1:def 19;
A3: rng(f*p) c= D by RELAT_1:def 19;
    dom f = A by A1,FUNCT_2:def 1;
    then f*p is FinSequence by A2,FINSEQ_1:16;
    hence thesis by A3,FINSEQ_1:def 4;
  end;
end;
