Set Bullet Behavior "Strict Subproofs".
Set Implicit Arguments.
Require Export FcEtt.ett_inf.
Require Export FcEtt.ett_ind.
(* This file contains these results:  -- the context is well-formed in any judgement -- all components are locally closed in any judgement *)
Hint Resolve DataTy_lc : lc.
destruct (CoercedValue_Value_lc_mutual); auto.
Qed.
destruct (CoercedValue_Value_lc_mutual); auto.
Qed.
Hint Resolve Value_lc CoercedValue_lc : lc.
(* -------------------------------- *)
Definition Typing_Ctx  := first  ctx_wff_mutual.
Definition PropWff_Ctx := second ctx_wff_mutual.
Definition Iso_Ctx     := third  ctx_wff_mutual.
Definition DefEq_Ctx   := fourth ctx_wff_mutual.
(* TODO: put these hints in a database? *)
Hint Resolve Typing_Ctx PropWff_Ctx Iso_Ctx DefEq_Ctx.
induction G; try auto.
inversion 1; subst; solve_uniq.
Qed.
Hint Resolve Ctx_uniq.
(* This version of the proof is incredibly slow. *)
(* all: pre; basic_solve. all: try oh_c'mon. all: try invert_open_wrt. all: try pick fresh c for L. all: try eapply lc_a_UCAbs_exists; eauto. all: try apply H; eauto. all: eapply (lc_a_UAbs_exists c). rewrite e. eauto. done. Qed.*)
Definition Typing_lc  := first lc_mutual.
Definition PropWff_lc := second lc_mutual.
Definition Iso_lc     := third lc_mutual.
Definition DefEq_lc   := fourth lc_mutual.
Definition Ctx_lc     := fifth lc_mutual.
Hint Resolve Typing_lc1 Typing_lc2 Iso_lc1 Iso_lc2 DefEq_lc1 DefEq_lc2 DefEq_lc3 Ctx_lc : lc.

Lemma Toplevel_lc : forall c s, binds c s toplevel -> lc_sig_sort s.