reserve a, I for set,
  S for non empty non void ManySortedSign;

theorem
  for A, B being non-empty MSAlgebra over S for F being
  ManySortedFunction of A, B st F is_monomorphism A, B holds A, Image F
  are_isomorphic
proof
  let A, B be non-empty MSAlgebra over S, F be ManySortedFunction of A, B;
  assume
A1: F is_monomorphism A, B;
  then F is_homomorphism A, B;
  then consider G being ManySortedFunction of A, Image F such that
A2: G = F and
A3: G is_epimorphism A, Image F by MSUALG_3:21;
  take G;
  thus G is_epimorphism A, Image F by A3;
  thus G is_homomorphism A, Image F by A3;
  thus thesis by A1,A2;
end;
