Require Export FcEtt.imports.
Require Export FcEtt.tactics.
Require Export FcEtt.ett_ott.
Require Export FcEtt.ett_inf.
Require Export FcEtt.ett_ind.
Require Export FcEtt.ett_par.
Require Export FcEtt.erase_syntax.
Module ext_consist (invert : ext_invert_sig)(fc_wf: fc_wf_sig).
Module red_one := ext_red_one invert.
Export red_one.
Module red := ext_red invert.
Export red.
Set Implicit Arguments.
Set Bullet Behavior "Strict Subproofs".
Definition Good (G : context) (D : available_props):=
erased_context G /\
forall c1 A B1 T1,
binds c1 (Co (Eq A B1 T1)) G
-> c1 `in` D
-> exists C, Par G D A C /\ Par G D B1 C.
(* ---------------------------------------- *)

Lemma a_Pi_head : forall S G b A rho B,
Par S G (a_Pi rho A B) b -> exists A' B' L,
b = a_Pi rho A' B' /\ Par S G A A' /\
(forall x, x `notin` L -> Par S G (open_tm_wrt_tm B (a_Var_f x)) (open_tm_wrt_tm B' (a_Var_f x))).