(**************************************************************************) (* ___ *) (* ||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 *) (* *) (**************************************************************************) 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 .