Local Notation "{ k ~> u } t" := (open_rec k u t) (at level 67).(*************************************************************************)
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(*  Coffee break                                                         *)
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(** * Typing environments *)
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(** We represent environments as association lists (lists of pairs of
    keys and values) whose keys are [atom]s.
*)

Notation env := (list (atom * typ)).

Lemma typing_c_to_lc_c : forall E e T, typing_c E e T -> lc_c e.