- V0 ➡ V1 → T0 ➡ T1 → ⋆. ⓓV1 ⊢ T1 [O,1] ▶ TT1 →
- T2 ➡ X2 → ⇧[O, 1] T2 ≡ T0 →
- ∃∃X. ⓓV1. TT1 ➡ X & X2 ➡ X.
-#X2 #V0 #V1 #T0 #T1 #TT1 #T2 #IH #_ #HT01 #HTT1 #HTX2 #HTT20
-elim (tpr_inv_lift … HT01 … HTT20) -HT01 #TT2 #HTT21 #HTT2
-lapply (tps_inv_lift1_eq … HTT1 … HTT21) -HTT1 #HTT1 destruct
-lapply (tw_lift … HTT20) -HTT20 #HTT20
-elim (IH … HTX2 … HTT2) -HTX2 -HTT2 -IH // /3 width=3/
+ V0 ➡ V1 → T0 ➡ T1 → ⋆. ⓓV1 ⊢ T1 ▶ [O,1] TT1 →
+ T0 ➡ T2 → ⇧[O, 1] X2 ≡ T2 →
+ ∃∃X. +ⓓV1. TT1 ➡ X & X2 ➡ X.
+#X2 #V0 #V1 #T0 #T1 #TT1 #T2 #IH #_ #HT01 #HTT1 #HT02 #HXT2
+elim (IH … HT01 … HT02) -IH -HT01 -HT02 // -V0 -T0 #T #HT1 #HT2
+elim (tpr_tps_bind ? ? V1 … HT1 HTT1) -T1 // #TT #HTT1 #HTT
+elim (tpr_inv_lift1 … HT2 … HXT2) -T2 #X #HXT #HX2
+lapply (tps_inv_lift1_eq … HTT … HXT) -HTT #H destruct /3 width=3/