reserve S for non empty non void ManySortedSign,
  V for non-empty ManySortedSet of the carrier of S,
  A for non-empty MSAlgebra over S,
  X for non empty Subset of S-Terms V,
  t for Element of X;
reserve S for non empty non void ManySortedSign,
  A for non-empty finite-yielding MSAlgebra over S,
  V for Variables of A,
  X for SetWithCompoundTerm of S,V;

theorem Th32:
  for S1, S2 being non empty ManySortedSign
  for f, g being Function st f, g form_morphism_between S1, S2
  holds f.:InnerVertices S1 c= InnerVertices S2
proof
  let S1, S2 be non empty ManySortedSign;
  let f, g be Function;
  assume f, g form_morphism_between S1, S2;
  then f*the ResultSort of S1 = (the ResultSort of S2)*g;
  then f.:InnerVertices S1 = rng ((the ResultSort of S2)*g) by RELAT_1:127;
  hence thesis by RELAT_1:26;
end;
