
theorem Th22:
  for S1,S2 being non empty ManySortedSign for A being non-empty
  MSAlgebra over S2 for f,g being Function st f,g form_morphism_between S1,S2
  holds A|(S1,f,g) is non-empty
proof
  let S1,S2 be non empty ManySortedSign;
  let A be non-empty MSAlgebra over S2;
  let f,g be Function;
  assume f,g form_morphism_between S1,S2;
  then the Sorts of (A|(S1,f,g)) = (the Sorts of A)*f by Def3;
  hence the Sorts of (A|(S1,f,g)) is non-empty;
end;
