-lemma cpx_lpx_aaa_conf: ∀h,o,G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A →
- ∀T2. ⦃G, L1⦄ ⊢ T1 ➡[h, o] T2 →
- ∀L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 → ⦃G, L2⦄ ⊢ T2 ⁝ A.
-#h #o #G #L1 #T1 #A #H elim H -G -L1 -T1 -A
-[ #o #L1 #s #X #H
- elim (cpx_inv_sort1 … H) -H // * //
-| #I #G #L1 #K1 #V1 #B #i #HLK1 #_ #IHV1 #X #H #L2 #HL12
- elim (cpx_inv_lref1 … H) -H
- [ #H destruct
- elim (lpx_drop_conf … HLK1 … HL12) -L1 #X #H #HLK2
- elim (lpx_inv_pair1 … H) -H
- #K2 #V2 #HK12 #HV12 #H destruct /3 width=6 by aaa_lref/
- | * #J #Y #Z #V2 #H #HV12 #HV2
- lapply (drop_mono … H … HLK1) -H #H destruct
- elim (lpx_drop_conf … HLK1 … HL12) -L1 #Z #H #HLK2
- elim (lpx_inv_pair1 … H) -H #K2 #V0 #HK12 #_ #H destruct
- /3 width=8 by aaa_lift, drop_fwd_drop2/
+(* Basic_2A1: was: cpx_lpx_aaa_conf *)
+lemma cpx_aaa_conf_lpx (h): ∀G,L1,T1,A. ⦃G,L1⦄ ⊢ T1 ⁝ A →
+ ∀T2. ⦃G,L1⦄ ⊢ T1 ⬈[h] T2 →
+ ∀L2. ⦃G,L1⦄ ⊢ ⬈[h] L2 → ⦃G,L2⦄ ⊢ T2 ⁝ A.
+#h #G #L1 #T1 #A #H elim H -G -L1 -T1 -A
+[ #G #L1 #s #X #H
+ elim (cpx_inv_sort1 … H) -H #H destruct //
+| #I #G #K1 #V1 #B #_ #IH #X #HX #Y #HY
+ elim (lpx_inv_pair_sn … HY) -HY #K2 #V2 #HK12 #HV12 #H destruct
+ elim (cpx_inv_zero1_pair … HX) -HX
+ [ #H destruct /3 width=1 by aaa_zero/
+ | * #V #HV1 #HVX -HV12
+ /4 width=7 by aaa_lifts, drops_refl, drops_drop, true/