Notation "s #1" := (fst s) (at level 9, format "s '#1'") : pair_scope.Notation "s #2" := (snd s) (at level 9, format "s '#2'") : pair_scope.Notation "t #l" := (t_left t) (at level 9, format "t '#l'") : pair_scope.Notation "t #b" := (t_in t) (at level 9, format "t '#b'") : pair_scope.Notation "t #r" := (t_right t) (at level 9, format "t '#r'") : pair_scope.

Lemma singleton_spec : forall x y, InT y (singleton x) <-> X.eq y x.