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 Th26:
  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 "\/" U1
proof
  let S be non void non empty ManySortedSign, U0 be non-empty MSAlgebra over S
  , U1,U2 be MSSubAlgebra of U0;
  reconsider u1= the Sorts of U1, u2= the Sorts of U2 as MSSubset of U0 by Def9
;
  u1 c= the Sorts of U0 & u2 c= the Sorts of U0 by PBOOLE:def 18;
  then u1 (\/) u2 c= the Sorts of U0 by PBOOLE:16;
  then reconsider A = u1 (\/) u2 as MSSubset of U0 by PBOOLE:def 18;
  U1 "\/" U2 = GenMSAlg(A) by Def18;
  hence thesis by Def18;
end;
