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 Th25:
  for S be non void non empty ManySortedSign, U0 be non-empty
  MSAlgebra over S, U1 be MSSubAlgebra of U0, B be MSSubset of U0 st B = the
  Sorts of U0 holds GenMSAlg(B) "\/" U1 = GenMSAlg(B)
proof
  let S be non void non empty ManySortedSign, U0 be non-empty MSAlgebra over S
  , U1 be MSSubAlgebra of U0, B be MSSubset of U0;
  assume
A1: B = the Sorts of U0;
  the Sorts of U1 is MSSubset of U0 by Def9;
  then the Sorts of U1 c= B by A1,PBOOLE:def 18;
  then B (\/) the Sorts of U1 = B by PBOOLE:22;
  hence thesis by Th24;
end;
