theorem
  for S being regular monotone OrderSortedSign, o being OperSymbol of
S, w1 being Element of (the carrier of S)* st w1 <= the_arity_of o holds LBound
  (o,w1) <= o
proof
  let S being regular monotone OrderSortedSign, o being OperSymbol of S, w1
  being Element of (the carrier of S)* such that
A1: w1 <= the_arity_of o;
  set lo = LBound(o,w1);
A2: lo has_least_rank_for o,w1 by A1,Th14;
  then lo has_least_sort_for o,w1;
  then
A3: the_result_sort_of lo <= the_result_sort_of o by A1;
A4: lo has_least_args_for o,w1 by A2;
  then
A5: o ~= lo;
  the_arity_of lo <= the_arity_of o by A1,A4;
  hence thesis by A5,A3;
end;
