theorem
  f in L1_Functions M & g in L1_Functions M implies (a.e-eq-class(f,M) =
  a.e-eq-class(g,M) iff g in a.e-eq-class(f,M))
proof
  assume
A1: f in L1_Functions M & g in L1_Functions M;
  then g a.e.= f,M iff g in a.e-eq-class(f,M) by Th37;
  hence thesis by A1,Th39;
end;
