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 Th66:
  for F being Function st [:rng p,{a}:] c= dom F holds F[:](p,a) is FinSequence
proof
  let F be Function;
  assume [:rng p,{a}:] c= dom F;
  then dom(F[:](p,a)) = dom p by Lm5;
  then dom(F[:](p,a)) = Seg len p by FINSEQ_1:def 3;
  hence thesis by FINSEQ_1:def 2;
end;
