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(** * Order on booleans *)
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#[global]
Hint Unfold le: bool.

Lemma le_implb : forall b1 b2, le b1 b2 <-> implb b1 b2 = true.
#[ local ] Definition lt (b1 b2:bool) :=
match b1 with
| true => False
| false => b2 = true
end.