reserve i for object;
reserve S for non empty ManySortedSign;
reserve D for non empty set,
  n for Nat;

theorem Th3:
  for h being homogeneous quasi_total non empty PartFunc of D*,D
  holds dom h = Funcs(Seg(arity h),D)
proof
  let h be homogeneous quasi_total non empty PartFunc of D*,D;
  thus dom h = (arity h)-tuples_on D by Lm1
    .= Funcs(Seg(arity h),D) by FINSEQ_2:93;
end;
