theorem
  f.a [= a implies lfp f [= a
proof
  assume
A1: f.a [= 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 Th31;
A3: lfp f [= (f, O)-.a by A2,Th43;
  (f, O)-.a [= a by A1,Th23;
  hence thesis by A3,LATTICES:7;
end;
