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(** * Order on booleans *)
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#[ local ] Definition le (b1 b2:bool) :=
  match b1 with
    | true => b2 = true
    | false => True
  end.

(* Specifications: *)
Lemma le_implb : forall b1 b2, le b1 b2 <-> implb b1 b2 = true.