matita/matita/contribs/lambdadelta/apps_2/etc/MLTT1/judgement.etc

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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/unfold/delift.ma".
  16 include "apps_2/MLTT1_1/genv_primitive.ma".
  17
  18 (* JUDJEMENTS ***************************************************************)
  19
  20 (* type judgement *)
  21 inductive TJ: lenv → predicate term ≝
  22 | tj_weak : ∀L,V,T1,T2. TJ L V → TJ L T1 → ⇧[0,1] T1 ≡ T2 → TJ (L Λ V) T2
  23 | tj_empty: TJ (⋆) 𝔼
  24 | tj_one  : TJ (⋆) 𝕆
  25 | tj_sum  : ∀G,A,B. TJ G A → TJ G B → TJ G (A ⊕ B)
  26 .
  27
  28 (* element judgement *)
  29 inductive EJ: lenv → relation term ≝
  30 | tj_erec: ∀L,V,T1,T2.
  31            EJ L V 𝔼 → TJ (L Λ 𝔼) T1 → L Δ V ⊢ T1 [0,1] ≡ T2 → EJ L 𝕖𝕣[V] T2
  32 | tj_tt  : EJ (⋆) 𝕥 𝕆
  33 .