reserve x,y for object;
reserve S for non void non empty ManySortedSign,
  o for OperSymbol of S,
  U0,U1, U2 for MSAlgebra over S;

theorem Th28:
  for S be non void non empty ManySortedSign, U0 be non-empty
  MSAlgebra over S, U1,U2 be MSSubAlgebra of U0 holds (U1 /\ U2)"\/"U2 =
  the MSAlgebra of U2
proof
  let S be non void non empty ManySortedSign, U0 be non-empty MSAlgebra over S
  , U1,U2 be MSSubAlgebra of U0;
  reconsider u12= the Sorts of (U1 /\ U2), u2 = the Sorts of U2 as MSSubset of
  U0 by Def9;
  u12 c= the Sorts of U0 & u2 c= the Sorts of U0 by PBOOLE:def 18;
  then u12 (\/) u2 c= the Sorts of U0 by PBOOLE:16;
  then reconsider A=u12 (\/) u2 as MSSubset of U0 by PBOOLE:def 18;
  u12 = (the Sorts of U1) (/\) (the Sorts of U2) by Def16;
  then u12 c= u2 by PBOOLE:15;
  then
A1: A = u2 by PBOOLE:22;
  (U1 /\ U2)"\/"U2=GenMSAlg(A) by Def18;
  hence thesis by A1,Th22;
end;
