#L #U1 #U2 #d #e #H #T1 #HTU1 @(tpss_ind … H) -U2 //
#U #U2 #_ #HU2 #IHU destruct
<(tps_inv_lift1_eq … HU2 … HTU1) -HU2 -HTU1 //
qed.
lemma tpss_inv_lift1_be_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫* U2 →
#L #U1 #U2 #d #e #H #T1 #HTU1 @(tpss_ind … H) -U2 //
#U #U2 #_ #HU2 #IHU destruct
<(tps_inv_lift1_eq … HU2 … HTU1) -HU2 -HTU1 //
qed.
lemma tpss_inv_lift1_be_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫* U2 →