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

theorem
  for A, B being non-empty MSAlgebra over S for C being non-empty
MSSubAlgebra of A for h1 being ManySortedFunction of B, C st h1 is_homomorphism
  B, C for h2 being ManySortedFunction of B, A st h1 = h2 holds h2
  is_homomorphism B, A
proof
  let A, B be non-empty MSAlgebra over S, C be non-empty MSSubAlgebra of A, h1
  be ManySortedFunction of B, C such that
A1: h1 is_homomorphism B, C;
  the Sorts of C is ManySortedSubset of the Sorts of A by MSUALG_2:def 9;
  then id (the Sorts of C) is ManySortedFunction of C, A by EXTENS_1:5;
  then consider G be ManySortedFunction of C, A such that
A2: G = id (the Sorts of C);
  G is_monomorphism C, A by A2,MSUALG_3:22;
  then
A3: G is_homomorphism C, A;
A4: G ** h1 = h1 by A2,MSUALG_3:4;
  let h2 be ManySortedFunction of B, A;
  assume h1 = h2;
  hence thesis by A1,A4,A3,MSUALG_3:10;
end;
