reserve a for set,
  i for Nat;

theorem Th12:
  for U1,U2 being Universal_Algebra st U1 is SubAlgebra of U2
  holds MSAlg U1 is MSSubAlgebra of MSAlg U2
proof
  let U1,U2 be Universal_Algebra;
  assume
A1: U1 is SubAlgebra of U2;
  then MSSign U1 = MSSign U2 by Th7;
  then reconsider A = MSAlg U1 as non-empty MSAlgebra over MSSign U2;
  A is MSSubAlgebra of MSAlg U2
  proof
    thus the Sorts of A is MSSubset of MSAlg U2 by A1,Th9;
    let B be MSSubset of MSAlg U2;
    assume
A2: B = the Sorts of A;
    hence B is opers_closed by A1,Th10;
    thus thesis by A1,A2,Th11;
  end;
  hence thesis;
end;
