(* Advanced properties ******************************************************)
(* Basic_1: was: nf2_lref_abst *)
-lemma cnr_lref_abst: â\88\80G,L,K,V,i. â\87©[i] L ≡ K. ⓛV → ⦃G, L⦄ ⊢ ➡ 𝐍⦃#i⦄.
+lemma cnr_lref_abst: â\88\80G,L,K,V,i. â¬\87[i] L ≡ K. ⓛV → ⦃G, L⦄ ⊢ ➡ 𝐍⦃#i⦄.
#G #L #K #V #i #HLK #X #H
elim (cpr_inv_lref1 … H) -H // *
#K0 #V1 #V2 #HLK0 #_ #_
(* Basic_1: was: nf2_lift *)
lemma cnr_lift: ∀G,L0,L,T,T0,s,d,e. ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄ →
- â\87©[s, d, e] L0 â\89¡ L â\86\92 â\87§[d, e] T ≡ T0 → ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄.
+ â¬\87[s, d, e] L0 â\89¡ L â\86\92 â¬\86[d, e] T ≡ T0 → ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄.
#G #L0 #L #T #T0 #s #d #e #HLT #HL0 #HT0 #X #H
elim (cpr_inv_lift1 … H … HL0 … HT0) -L0 #T1 #HT10 #HT1
<(HLT … HT1) in HT0; -L #HT0
(* Note: this was missing in basic_1 *)
lemma cnr_inv_lift: ∀G,L0,L,T,T0,s,d,e. ⦃G, L0⦄ ⊢ ➡ 𝐍⦃T0⦄ →
- â\87©[s, d, e] L0 â\89¡ L â\86\92 â\87§[d, e] T ≡ T0 → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄.
+ â¬\87[s, d, e] L0 â\89¡ L â\86\92 â¬\86[d, e] T ≡ T0 → ⦃G, L⦄ ⊢ ➡ 𝐍⦃T⦄.
#G #L0 #L #T #T0 #s #d #e #HLT0 #HL0 #HT0 #X #H
elim (lift_total X d e) #X0 #HX0
lapply (cpr_lift … H … HL0 … HT0 … HX0) -L #HTX0