(* activate genv *)
(* reducible terms *)
inductive crr (G:genv): relation2 lenv term ≝
-| crr_delta : â\88\80L,K,V,i. â\87©[i] L ≡ K.ⓓV → crr G L (#i)
+| crr_delta : â\88\80L,K,V,i. â¬\87[i] L ≡ K.ⓓV → crr G L (#i)
| crr_appl_sn: ∀L,V,T. crr G L V → crr G L (ⓐV.T)
| crr_appl_dx: ∀L,V,T. crr G L T → crr G L (ⓐV.T)
| crr_ri2 : ∀I,L,V,T. ri2 I → crr G L (②{I}V.T)
/2 width=6 by crr_inv_sort_aux/ qed-.
fact crr_inv_lref_aux: ∀G,L,T,i. ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ → T = #i →
- â\88\83â\88\83K,V. â\87©[i] L ≡ K.ⓓV.
+ â\88\83â\88\83K,V. â¬\87[i] L ≡ K.ⓓV.
#G #L #T #j * -L -T
[ #L #K #V #i #HLK #H destruct /2 width=3 by ex1_2_intro/
| #L #V #T #_ #H destruct
]
qed-.
-lemma crr_inv_lref: â\88\80G,L,i. â¦\83G, Lâ¦\84 â\8a¢ â\9e¡ ð\9d\90\91â¦\83#iâ¦\84 â\86\92 â\88\83â\88\83K,V. â\87©[i] L ≡ K.ⓓV.
+lemma crr_inv_lref: â\88\80G,L,i. â¦\83G, Lâ¦\84 â\8a¢ â\9e¡ ð\9d\90\91â¦\83#iâ¦\84 â\86\92 â\88\83â\88\83K,V. â¬\87[i] L ≡ K.ⓓV.
/2 width=4 by crr_inv_lref_aux/ qed-.
fact crr_inv_gref_aux: ∀G,L,T,p. ⦃G, L⦄ ⊢ ➡ 𝐑⦃T⦄ → T = §p → ⊥.