
theorem Th6:
  for S being non empty non void ManySortedSign
  for A being non-empty MSAlgebra over S
  holds A is image of A
  proof
    let S be non empty non void ManySortedSign;
    let A be non-empty MSAlgebra over S;
    A is A-Image
    proof
      now
        take B = A;
        reconsider h = id the Sorts of A as ManySortedFunction of
        the Sorts of A, the Sorts of B;
        take h;
        thus h is_homomorphism A,B by MSUALG_3:9;
        thus the MSAlgebra of A = Image h by Th5;
      end;
      hence thesis by MSAFREE4:def 4;
    end;
    hence thesis;
  end;
