reserve i for Nat, x,y for set;
reserve S for non empty non void ManySortedSign;
reserve X for non-empty ManySortedSet of S;

theorem Th32:
  for S being non empty non void ManySortedSign
  for A,B being MSAlgebra over S st the MSAlgebra of A = the MSAlgebra of B
  for G being GeneratorSet of A holds G is GeneratorSet of B
  proof
    let S be non empty non void ManySortedSign;
    let A,B be MSAlgebra over S such that
A1: the MSAlgebra of A = the MSAlgebra of B;
    let G be GeneratorSet of A;
    reconsider H = G as MSSubset of B by A1;
    GenMSAlg H = GenMSAlg G by A1,Th31;
    hence G is GeneratorSet of B by A1,MSAFREE:def 4;
  end;
