(* extended reducible terms *)
inductive crx (h) (g) (G:genv): relation2 lenv term ≝
| crx_sort : ∀L,k,l. deg h g k (l+1) → crx h g G L (⋆k)
-| crx_delta : â\88\80I,L,K,V,i. â\87©[i] L ≡ K.ⓑ{I}V → crx h g G L (#i)
+| crx_delta : â\88\80I,L,K,V,i. â¬\87[i] L ≡ K.ⓑ{I}V → crx h g G L (#i)
| crx_appl_sn: ∀L,V,T. crx h g G L V → crx h g G L (ⓐV.T)
| crx_appl_dx: ∀L,V,T. crx h g G L T → crx h g G L (ⓐV.T)
| crx_ri2 : ∀I,L,V,T. ri2 I → crx h g G L (②{I}V.T)
/2 width=5 by crx_inv_sort_aux/ qed-.
fact crx_inv_lref_aux: ∀h,g,G,L,T,i. ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄ → T = #i →
- â\88\83â\88\83I,K,V. â\87©[i] L ≡ K.ⓑ{I}V.
+ â\88\83â\88\83I,K,V. â¬\87[i] L ≡ K.ⓑ{I}V.
#h #g #G #L #T #j * -L -T
[ #L #k #l #_ #H destruct
| #I #L #K #V #i #HLK #H destruct /2 width=4 by ex1_3_intro/
]
qed-.
-lemma crx_inv_lref: â\88\80h,g,G,L,i. â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h, g] ð\9d\90\91â¦\83#iâ¦\84 â\86\92 â\88\83â\88\83I,K,V. â\87©[i] L ≡ K.ⓑ{I}V.
+lemma crx_inv_lref: â\88\80h,g,G,L,i. â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h, g] ð\9d\90\91â¦\83#iâ¦\84 â\86\92 â\88\83â\88\83I,K,V. â¬\87[i] L ≡ K.ⓑ{I}V.
/2 width=6 by crx_inv_lref_aux/ qed-.
fact crx_inv_gref_aux: ∀h,g,G,L,T,p. ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄ → T = §p → ⊥.