theorem
  a [= f.a implies a [= gfp f
proof
  assume
A1: a [= f.a;
  then consider O such that
  card O c= card the carrier of L and
A2: (f, O)+.a is_a_fixpoint_of f by Th30;
A3: (f, O)+.a [= gfp f by A2,Th43;
  a [= (f, O)+.a by A1,Th22;
  hence thesis by A3,LATTICES:7;
end;
