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 Th10:
  for D being set holds (for i being Nat st i in dom p holds p.i in D)
  implies p is FinSequence of D
proof
  let D be set;
  assume
A1: for i being Nat st i in dom p holds p.i in D;
  let b be object;
  assume b in rng p;
  then ex i being Nat st i in dom p & p.i = b by Th8;
  hence thesis by A1;
end;
