(* Advanced properties ******************************************************)
-(* Basic_1: was: nf2_lref_abst *)
lemma cnr_lref_abst: ∀G,L,K,V,i. ⬇[i] L ≡ K. ⓛV → ⦃G, L⦄ ⊢ ➡ 𝐍⦃#i⦄.
#G #L #K #V #i #HLK #X #H
elim (cpr_inv_lref1 … H) -H // *
(* Relocation properties ****************************************************)
-(* Basic_1: was: nf2_lift *)
lemma cnr_lift: ∀G,L0,L,T,T0,s,l,m. ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ →
⬇[s, l, m] L0 ≡ L → ⬆[l, m] T ≡ T0 → ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄.
#G #L0 #L #T #T0 #s #l #m #HLT #HL0 #HT0 #X #H
>(lift_mono … HT10 … HT0) -T1 -X //
qed.
-(* Note: this was missing in basic_1 *)
lemma cnr_inv_lift: ∀G,L0,L,T,T0,s,l,m. ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄ →
⬇[s, l, m] L0 ≡ L → ⬆[l, m] T ≡ T0 → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄.
#G #L0 #L #T #T0 #s #l #m #HLT0 #HL0 #HT0 #X #H