reserve U0,U1,U2,U3 for Universal_Algebra,
  n for Nat,
  x,y for set;
reserve A for non empty Subset of U0,
  o for operation of U0,
  x1,y1 for FinSequence of A;

theorem Th23:
  for U0 be with_const_op Universal_Algebra,U1,U2 be strict
  SubAlgebra of U0 holds (U1 /\ U2)"\/"U2 = U2
proof
  let U0 be with_const_op Universal_Algebra, U1,U2 be strict SubAlgebra of U0;
  reconsider u12= the carrier of (U1 /\ U2), u2 = the carrier of U2 as non
  empty Subset of U0 by Def7;
  reconsider A=u12 \/ u2 as non empty Subset of U0;
  (the carrier of U1) meets (the carrier of U2) by Th17;
  then u12 = (the carrier of U1) /\ (the carrier of U2) by Def9;
  then
A1: u12 c= u2 by XBOOLE_1:17;
  (U1 /\ U2)"\/"U2=GenUnivAlg(A) by Def13;
  hence thesis by A1,Th19,XBOOLE_1:12;
end;
