reserve S for non void non empty ManySortedSign,
  U1, U2, U3 for non-empty MSAlgebra over S,
  I for set,
  A for ManySortedSet of I,
  B, C for non-empty ManySortedSet of I;

theorem
  for U1 being MSAlgebra over S, U2 being MSSubAlgebra of U1 for B1
  being MSSubset of U1, B2 being MSSubset of U2 st B1 = B2 holds GenMSAlg B1 =
  GenMSAlg B2
proof
  let U1 be MSAlgebra over S, U2 be MSSubAlgebra of U1, B1 be MSSubset of U1,
  B2 be MSSubset of U2 such that
A1: B1 = B2;
  reconsider H = GenMSAlg B1 as MSSubAlgebra of U2 by A1,MSUALG_2:def 17;
  reconsider G = GenMSAlg B2 as MSSubAlgebra of U1 by MSUALG_2:6;
  B1 is MSSubset of G by A1,MSUALG_2:def 17;
  then
A2: GenMSAlg B1 is MSSubAlgebra of G by MSUALG_2:def 17;
  B1 is MSSubset of H by MSUALG_2:def 17;
  then GenMSAlg B2 is MSSubAlgebra of GenMSAlg B1 by A1,MSUALG_2:def 17;
  hence thesis by A2,MSUALG_2:7;
end;
