theorem Th98:
  for R being NF-var terminating with_UN_property invariant stable
  ManySortedRelation of Free(S,X)
  for o,p holds R.the_result_sort_of o reduces o-term p,
  Den(o,NFAlgebra R).((canonical_homomorphism NFAlgebra R)#p)
  proof
    let R be NF-var terminating with_UN_property invariant stable
    ManySortedRelation of Free(S,X);
    let o,p;
    set T = NFAlgebra R;
    set h = canonical_homomorphism T;
A1: o-term p = Den(o,Free(S,X)).p by MSAFREE4:13;
A2: the_sort_of (o-term p) = the_result_sort_of o by Th8;
    h.(the_result_sort_of o).(o-term p) = Den(o,T).(h#p)
    by A1,MSUALG_3:def 7,MSAFREE4:def 10;
    then Den(o,T).(h#p) = h.(o-term p) by A2,ABBR;
    hence R.the_result_sort_of o reduces o-term p, Den(o,T).(h#p) by A2,Th90;
  end;
