reserve S for non empty non void ManySortedSign;
reserve X for non-empty ManySortedSet of S;
reserve x,y,z for set, i,j for Nat;
reserve
  A0 for (X,S)-terms non-empty MSAlgebra over S,
  A1 for all_vars_including (X,S)-terms MSAlgebra over S,
  A2 for all_vars_including inheriting_operations (X,S)-terms MSAlgebra over S,
  A for all_vars_including inheriting_operations free_in_itself
  (X,S)-terms MSAlgebra over S;
reserve X0 for non-empty countable ManySortedSet of S;
reserve A0 for all_vars_including inheriting_operations free_in_itself
  (X0,S)-terms MSAlgebra over S;

theorem Th79:
  for R being terminating with_UN_property invariant stable
  ManySortedRelation of Free(S,X)
  for a being SortSymbol of S
  st x in (NForms R).a holds nf(x,R.a) = x
  proof
    let R be terminating with_UN_property invariant stable
    ManySortedRelation of Free(S,X);
    let a be SortSymbol of S;
    assume x in (NForms R).a;
    then x in the set of all nf(z,R.a) where z is Element of Free(S,X),a
    by Def19;
    then ex z being Element of Free(S,X),a st x = nf(z,R.a);
    hence nf(x,R.a) = x by Th18;
  end;
