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 Th34:
  for OU0 being strict OSAlgebra of S1 for B being OSSubset of OU0
  st B = the Sorts of OU0 holds GenOSAlg(B) = OU0
proof
  let OU0 be strict OSAlgebra of S1;
  let B be OSSubset of OU0;
  assume B = the Sorts of OU0;
  then
A1: GenMSAlg(B) = OU0 by MSUALG_2:21;
  GenMSAlg(B) is strict MSSubAlgebra of GenOSAlg(B) by Th32,MSUALG_2:8;
  hence thesis by A1,MSUALG_2:7;
end;
