(* Properties with generic slicing ******************************************)
-lemma cnx_lref_atom: ∀h,G,L,i. ⬇*[i] L ≘ ⋆ → ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃#i⦄.
+lemma cnx_lref_atom: ∀h,G,L,i. ⬇*[i] L ≘ ⋆ → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃#i⦄.
#h #G #L #i #Hi #X #H elim (cpx_inv_lref1_drops … H) -H // *
#I #K #V1 #V2 #HLK lapply (drops_mono … Hi … HLK) -L #H destruct
qed.
-lemma cnx_lref_unit: ∀h,I,G,L,K,i. ⬇*[i] L ≘ K.ⓤ{I} → ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃#i⦄.
+lemma cnx_lref_unit: ∀h,I,G,L,K,i. ⬇*[i] L ≘ K.ⓤ{I} → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃#i⦄.
#h #I #G #L #K #i #HLK #X #H elim (cpx_inv_lref1_drops … H) -H // *
#Z #Y #V1 #V2 #HLY lapply (drops_mono … HLK … HLY) -L #H destruct
qed.
(* Inversion lemmas with generic slicing ************************************)
(* Basic_2A1: was: cnx_inv_delta *)
-lemma cnx_inv_lref_pair: ∀h,I,G,L,K,V,i. ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃#i⦄ → ⊥.
+lemma cnx_inv_lref_pair: ∀h,I,G,L,K,V,i. ⬇*[i] L ≘ K.ⓑ{I}V → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃#i⦄ → ⊥.
#h #I #G #L #K #V #i #HLK #H
elim (lifts_total V (𝐔❴↑i❵)) #W #HVW
lapply (H W ?) -H /2 width=7 by cpx_delta_drops/ -HLK