(* Basic_1: was only: nf2_csort_lref *)
lemma cnr_lref_atom (h) (b) (G) (L):
- â\88\80i. â\87©*[b,ð\9d\90\94â\9d´iâ\9dµ] L â\89\98 â\8b\86 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â\9e¡[h] ð\9d\90\8dâ¦\83#iâ¦\84.
+ â\88\80i. â\87©*[b,ð\9d\90\94â\9d¨iâ\9d©] L â\89\98 â\8b\86 â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] ð\9d\90\8dâ\9dª#iâ\9d«.
#h #b #G #L #i #Hi #X #H
elim (cpr_inv_lref1_drops … H) -H // * #K #V1 #V2 #HLK
lapply (drops_gen b … HLK) -HLK #HLK
(* Basic_1: was: nf2_lref_abst *)
lemma cnr_lref_abst (h) (G) (L):
- ∀K,V,i. ⇩*[i] L ≘ K.ⓛV → ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃#i⦄.
+ ∀K,V,i. ⇩[i] L ≘ K.ⓛV → ❪G,L❫ ⊢ ➡[h] 𝐍❪#i❫.
#h #G #L #K #V #i #HLK #X #H
elim (cpr_inv_lref1_drops … H) -H // *
#K0 #V1 #V2 #HLK0 #_ #_
qed.
lemma cnr_lref_unit (h) (I) (G) (L):
- ∀K,i. ⇩*[i] L ≘ K.ⓤ{I} → ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃#i⦄.
+ ∀K,i. ⇩[i] L ≘ K.ⓤ[I] → ❪G,L❫ ⊢ ➡[h] 𝐍❪#i❫.
#h #I #G #L #K #i #HLK #X #H
elim (cpr_inv_lref1_drops … H) -H // *
#K0 #V1 #V2 #HLK0 #_ #_
(* Basic_2A1: was: cnr_inv_delta *)
lemma cnr_inv_lref_abbr (h) (G) (L):
- ∀K,V,i. ⇩*[i] L ≘ K.ⓓV → ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃#i⦄ → ⊥.
+ ∀K,V,i. ⇩[i] L ≘ K.ⓓV → ❪G,L❫ ⊢ ➡[h] 𝐍❪#i❫ → ⊥.
#h #G #L #K #V #i #HLK #H
-elim (lifts_total V ð\9d\90\94â\9d´â\86\91iâ\9dµ) #W #HVW
+elim (lifts_total V ð\9d\90\94â\9d¨â\86\91iâ\9d©) #W #HVW
lapply (H W ?) -H [ /3 width=6 by cpm_delta_drops/ ] -HLK #H destruct
elim (lifts_inv_lref2_uni_lt … HVW) -HVW //
qed-.