theorem Th86:
  ex g being Endomorphism of T st
  (canonical_homomorphism T)**h = g**canonical_homomorphism T &
  for t being Element of T holds g.t = (canonical_homomorphism T).(h.@t)
  proof set H = canonical_homomorphism T;
    H is_homomorphism Free(S,X),T & h is_homomorphism Free(S,X),Free(S,X)
    by MSUALG_6:def 2,MSAFREE4:def 10;
    then consider g being ManySortedFunction of T,T such that
A1: g is_homomorphism T,T & H**h = g**H by MSAFREE4:65,MSUALG_3:10;
    reconsider g as Endomorphism of T by A1,MSUALG_6:def 2;
    take g;
    thus H**h = g**H by A1;
    let t be Element of T;
    thus g.t = g.(H.@t)
    .= (g**H).@t by Th14
    .= (canonical_homomorphism T).(h.@t) by A1,Th14;
  end;
