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 Th62:
  for F being Function st [:rng p,rng q:] c= dom F holds F.:(p,q)
  is FinSequence
proof
  let F be Function;
  reconsider k = min(len p,len q) as Element of NAT by XXREAL_0:15;
  assume [:rng p,rng q:] c= dom F;
  then dom(F.:(p,q)) = Seg k by Lm3;
  hence thesis by FINSEQ_1:def 2;
end;
