theorem Th28:
  for h being ManySortedFunction of T,C st h is_homomorphism T,C
  for a being SortSymbol of S
  for t being Element of T,a
  holds t value_at(C,h||FreeGen T) = h.a.t
  proof
    let h be ManySortedFunction of T,C;
    assume A1: h is_homomorphism T,C;
    set s = h||FreeGen T;
    let a be SortSymbol of S;
    let t be Element of T,a;
    FreeGen T is_transformable_to the Sorts of C by MSAFREE4:21;
    then
A2: doms s = FreeGen T by MSSUBFAM:17;
    thus t value_at(C,s) = h.a.t by A2,A1,AOFA_A00:def 21;
  end;
