+#L #T0 #T1 #d #e #H elim H -H L T0 T1 d e
+[ /2/
+| /2/
+| #L #K1 #V1 #W1 #T1 #i1 #d #e #Hdi1 #Hi1de #HLK1 #HVW1 #HWT1 #IHVW1 #T2 #H
+ elim (tps_inv_lref1 … H) -H
+ [ -IHVW1 #HX destruct -T2
+ @ex2_1_intro [2: // | skip ] /2 width=6/ (**) (* /3 width=9/ is slow *)
+ | * #K2 #V2 #W2 #i2 #Hdi2 #Hi2de #HLK2 #HVW2 #HWT2
+ elim (lt_or_eq_or_gt i1 i2) #Hi12
+ [ @tps_conf_subst_subst_lt /width=19/
+ | -HVW1; destruct -i2;
+ lapply (transitive_le ? ? (i1 + 1) Hdi2 ?) -Hdi2 // #Hdi2
+ lapply (drop_mono … HLK1 … HLK2) -HLK1 Hdi1 Hi1de #H destruct -V1 K1;
+ elim (IHVW1 … HVW2) -IHVW1 HVW2 #W #HW1 #HW2
+ lapply (drop_fwd_drop2 … HLK2) -HLK2 #HLK2
+ elim (lift_total W 0 (i1 + 1)) #T #HWT
+ lapply (tps_lift_ge … HW1 … HLK2 HWT1 HWT ?) -HW1 HWT1 //
+ lapply (tps_lift_ge … HW2 … HLK2 HWT2 HWT ?) -HW2 HWT2 HLK2 HWT // normalize #HT2 #HT1
+ lapply (tps_weak … HT1 d e ? ?) -HT1 [ >arith_i2 // | // ]
+ lapply (tps_weak … HT2 d e ? ?) -HT2 [ >arith_i2 // | // ]
+ /2/
+ | @ex2_1_comm @tps_conf_subst_subst_lt /width=19/
+ ]
+ ]
+| #L #I #V0 #V1 #T0 #T1 #d #e #_ #_ #IHV01 #IHT01 #X #HX
+ elim (tps_inv_bind1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
+ elim (IHV01 … HV02) -IHV01 HV02 #V #HV1 #HV2
+ elim (IHT01 … HT02) -IHT01 HT02 #T #HT1 #HT2
+ @ex2_1_intro
+ [2: @tps_bind [4: @(tps_leq_repl … HT1) /2/ |2: skip ]
+ |1: skip
+ |3: @tps_bind [2: @(tps_leq_repl … HT2) /2/ ]
+ ] // (**) (* /5/ is too slow *)
+| #L #I #V0 #V1 #T0 #T1 #d #e #_ #_ #IHV01 #IHT01 #X #HX
+ elim (tps_inv_flat1 … HX) -HX #V2 #T2 #HV02 #HT02 #HX destruct -X;
+ elim (IHV01 … HV02) -IHV01 HV02;
+ elim (IHT01 … HT02) -IHT01 HT02 /3 width=5/
+]
+qed.