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(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
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include "basic_2/unfold/delift.ma".
include "apps_2/MLTT1_1/genv_primitive.ma".

(* JUDJEMENTS ***************************************************************)

(* type judgement *)
inductive TJ: lenv → predicate term ≝
| tj_weak : ∀L,V,T1,T2. TJ L V → TJ L T1 → ⇧[0,1] T1 ≡ T2 → TJ (L Λ V) T2
| tj_empty: TJ (⋆) 𝔼
| tj_one  : TJ (⋆) 𝕆
| tj_sum  : ∀G,A,B. TJ G A → TJ G B → TJ G (A ⊕ B)
.

(* element judgement *)
inductive EJ: lenv → relation term ≝
| tj_erec: ∀L,V,T1,T2. 
           EJ L V 𝔼 → TJ (L Λ 𝔼) T1 → L Δ V ⊢ T1 [0,1] ≡ T2 → EJ L 𝕖𝕣[V] T2
| tj_tt  : EJ (⋆) 𝕥 𝕆
.