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 Th45:
  for p being FinSequence of D for f being Function of dom p,dom p
  holds p*f is FinSequence of D
proof
  let p be FinSequence of D;
  Seg len p = dom p by FINSEQ_1:def 3;
  hence thesis by Th43;
end;
