∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄.
#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
/3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, lpr_pair, cpr_pair_sn, cpr_atom, cpr_bind, cpr_flat, ex3_2_intro/
-#G #L #K #U #T #e #HLK #HUT #U2 #HU2
-elim (lift_total U2 0 (e+1)) #T2 #HUT2
+#G #L #K #U #T #m #HLK #HUT #U2 #HU2
+elim (lift_total U2 0 (m+1)) #T2 #HUT2
lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9 by fqu_drop, ex3_2_intro/
qed-.
∃∃L,U1. ⦃G1, L1⦄ ⊢ ➡ L & ⦃G1, L1⦄ ⊢ T1 ➡ U1 & ⦃G1, L, U1⦄ ⊐ ⦃G2, L2, U2⦄.
#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
/3 width=5 by fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, lpr_pair, cpr_pair_sn, cpr_atom, cpr_bind, cpr_flat, ex3_2_intro/
-#G #L #K #U #T #e #HLK #HUT #U2 #HU2
-elim (lift_total U2 0 (e+1)) #T2 #HUT2
+#G #L #K #U #T #m #HLK #HUT #U2 #HU2
+elim (lift_total U2 0 (m+1)) #T2 #HUT2
lapply (cpr_lift … HU2 … HLK … HUT … HUT2) -HU2 -HUT /3 width=9 by fqu_drop, ex3_2_intro/
qed-.
[ #a #I #G2 #L2 #V2 #T2 #X #H elim (lpr_inv_pair1 … H) -H
#K2 #W2 #HLK2 #HVW2 #H destruct
/3 width=5 by fqu_fquq, cpr_pair_sn, fqu_bind_dx, ex3_2_intro/
-| #G #L1 #K1 #T1 #U1 #e #HLK1 #HTU1 #K2 #HK12
+| #G #L1 #K1 #T1 #U1 #m #HLK1 #HTU1 #K2 #HK12
elim (drop_lpr_trans … HLK1 … HK12) -HK12
/3 width=7 by fqu_drop, ex3_2_intro/
]