lemma lsx_lref_be_lpxs: ∀h,g,I,G,K1,V,i,d. d ≤ yinj i → ⦃G, K1⦄ ⊢ ⬊*[h, g] V →
∀K2. G ⊢ ⬊*[h, g, V, 0] K2 → ⦃G, K1⦄ ⊢ ➡*[h, g] K2 →
- â\88\80L2. â\87©[i] L2 ≡ K2.ⓑ{I}V → G ⊢ ⬊*[h, g, #i, d] L2.
+ â\88\80L2. â¬\87[i] L2 ≡ K2.ⓑ{I}V → G ⊢ ⬊*[h, g, #i, d] L2.
#h #g #I #G #K1 #V #i #d #Hdi #H @(csx_ind_alt … H) -V
#V0 #_ #IHV0 #K2 #H @(lsx_ind … H) -K2
#K0 #HK0 #IHK0 #HK10 #L0 #HLK0 @lsx_intro
-#L2 #HL02 #HnL02 elim (lpx_ldrop_conf … HLK0 … HL02) -HL02
+#L2 #HL02 #HnL02 elim (lpx_drop_conf … HLK0 … HL02) -HL02
#Y #H #HLK2 elim (lpx_inv_pair1 … H) -H
#K2 #V2 #HK02 #HV02 #H destruct
elim (eq_term_dec V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnL02 -HLK0 ]
lemma lsx_lref_be: ∀h,g,I,G,K,V,i,d. d ≤ yinj i → ⦃G, K⦄ ⊢ ⬊*[h, g] V →
G ⊢ ⬊*[h, g, V, 0] K →
- â\88\80L. â\87©[i] L ≡ K.ⓑ{I}V → G ⊢ ⬊*[h, g, #i, d] L.
+ â\88\80L. â¬\87[i] L ≡ K.ⓑ{I}V → G ⊢ ⬊*[h, g, #i, d] L.
/2 width=8 by lsx_lref_be_lpxs/ qed.
(* Main properties **********************************************************)
[ #i #HG #HL #HT #H #d destruct
elim (lt_or_ge i (|L|)) /2 width=1 by lsx_lref_free/
elim (ylt_split i d) /2 width=1 by lsx_lref_skip/
- #Hdi #Hi elim (ldrop_O1_lt … Hi) -Hi
+ #Hdi #Hi elim (drop_O1_lt (Ⓕ) … Hi) -Hi
#I #K #V #HLK lapply (csx_inv_lref_bind … HLK … H) -H
/4 width=6 by lsx_lref_be, fqup_lref/
| #a #I #V #T #HG #HL #HT #H #d destruct