reserve U0 for Universal_Algebra,
  U1 for SubAlgebra of U0,
  o for operation of U0;

theorem Th18:
  for U0 being with_const_op strict Universal_Algebra for U1 be
  strict SubAlgebra of U0 holds GenUnivAlg(Constants(U0)) /\ U1 = GenUnivAlg(
  Constants(U0))
proof
  let U0 be with_const_op strict Universal_Algebra;
  let U1 be strict SubAlgebra of U0;
  set C = Constants(U0), G = GenUnivAlg(C);
  C is Subset of U1 by UNIALG_2:15;
  then G is strict SubAlgebra of U1 by UNIALG_2:def 12;
  then
A1: the carrier of G is Subset of U1 by UNIALG_2:def 7;
  (the carrier of G) meets (the carrier of U1) by UNIALG_2:17;
  then the carrier of ( G /\ U1) = (the carrier of G) /\ (the carrier of U1 )
  by UNIALG_2:def 9;
  hence thesis by A1,UNIALG_2:12,XBOOLE_1:28;
end;
