-lemma tps_fwd_shift1: ∀L1,L,T1,T,d,e. L ⊢ L1 @@ T1 ▶ [d, e] T →
- ∃∃L2,T2. L1 𝟙 L2 & T = L2 @@ T2.
-#L1 @(lenv_ind_dx … L1) -L1
-[ #L #T1 #T #d #e #_ @ex2_2_intro [3: // |4: // |1,2: skip ] (**) (* /2 width=4/ does not work *)
-| #I #L1 #V1 #IH #L #T1 #T #d #e >shift_append_assoc #H
- elim (tps_inv_bind1 … H) -H #V2 #T2 #_ #HT12 #H destruct
- elim (IH … HT12) -IH -L -T1 -d -e #L2 #T #HL12 #H destruct
- @(ex2_2_intro … (⋆.ⓑ{I}V2@@L2)) /2 width=4/ /3 width=2/
-]
-qed-.
-