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;
reserve U0 for non-empty MSAlgebra over S;

theorem
  for S be non void non empty ManySortedSign, U0 be non-empty
  MSAlgebra over S holds Top (MSSubAlLattice(U0)) = the MSAlgebra of U0
proof
  let S be non void non empty ManySortedSign, U0 be non-empty MSAlgebra
  over S;
  reconsider B = the Sorts of U0 as MSSubset of U0 by PBOOLE:def 18;
  thus Top (MSSubAlLattice(U0)) = GenMSAlg(B) by Th35
    .= the MSAlgebra of U0 by Th21;
end;
