reserve S for non empty non void ManySortedSign,
  A for MSAlgebra over S;
reserve A for non-empty MSAlgebra over S;

theorem
  for h being Endomorphism of A for o being OperSymbol of S, i being
  Element of NAT st i in dom the_arity_of o for a being Element of Args(o,A)
  holds (h.the_result_sort_of o)*transl(o,i,a,A) = transl(o,i,h#a,A)*(h.((
  the_arity_of o)/.i))
by Def2,Th21;
