Notation reflect := Datatypes.reflect.Notation ReflectT := Datatypes.ReflectT.Notation ReflectF := Datatypes.ReflectF.(**  An alternative to xorb that behaves somewhat better wrt simplification. **)
Definition addb b := if b then negb else id.(**  Notation for && and || is declared in Init.Datatypes.  **)
Notation "~~ b" := (negb b) : bool_scope.Notation "b ==> c" := (implb b c) : bool_scope.Notation "b1 (+) b2" := (addb b1 b2) : bool_scope.Ltac prop_congr := apply: prop_congr.

Lemma not_false_is_true : ~ false.