reserve U1,U2,U3 for Universal_Algebra,
  n,m for Nat,
  x,y,z for object,
  A,B for non empty set,
  h1 for FinSequence of [:A,B:];
reserve h1 for homogeneous quasi_total non empty PartFunc of
    (the carrier of U1)*,the carrier of U1,
  h2 for homogeneous quasi_total non empty PartFunc of
    (the carrier of U2)*,the carrier of U2;

theorem Th10:
  for f be FinSequence of NAT st f <> {} holds UAStr (#{{}},
    TrivialOps(f)#) is strict Universal_Algebra
proof
  let f be FinSequence of NAT;
  assume
A1: f <> {};
  set U0 = UAStr (#{{}},TrivialOps(f)#);
A2: the charact of U0 is homogeneous quasi_total non-empty by Th9;
  len (the charact of U0) = len f by Def8;
  then the charact of U0 <> {} by A1;
  hence thesis by A2,UNIALG_1:def 1,def 2,def 3;
end;
