reserve x for set,
  R for non empty Poset;
reserve S1 for OrderSortedSign,
  OU0 for OSAlgebra of S1;
reserve s,s1,s2,s3,s4 for SortSymbol of S1;

theorem Th36:
  for U0 be non-empty OSAlgebra of S1, U1 be OSSubAlgebra of U0
  holds GenOSAlg(OSConstants(U0)) /\ U1 = GenOSAlg(OSConstants(U0))
proof
  let U0 be non-empty OSAlgebra of S1, U1 be OSSubAlgebra of U0;
  set C = OSConstants(U0), G = GenOSAlg(C);
  C is OSSubset of U1 by Th13;
  then G is strict OSSubAlgebra of U1 by Def12;
  then the Sorts of G is MSSubset of U1 by MSUALG_2:def 9;
  then the Sorts of ( G /\ U1) = (the Sorts of G) (/\) (the Sorts of U1) & the
  Sorts of G c= the Sorts of U1 by MSUALG_2:def 16,PBOOLE:def 18;
  then the Sorts of ( G /\ U1) = the Sorts of G by PBOOLE:23;
  hence thesis by MSUALG_2:9;
end;
