reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem Th31:
  for p being FinSequence of A
  for f being Function of A,D9 st q = f*p holds len q = len p
proof
  let p be FinSequence of A;
  let f be Function of A,D9;
  dom f = A & rng p c= A by FINSEQ_1:def 4,FUNCT_2:def 1;
  hence thesis by Th27;
end;
