(* *)
(**************************************************************************)
+include "basic_2/grammar/lenv_top.ma".
include "basic_2/substitution/ldrop.ma".
(* PARALLEL SUBSTITUTION ON TERMS *******************************************)
/3 by monotonic_le_plus_l, le_plus/ (**) (* just /3 width=1/ is too slow *)
qed-.
+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-.
+
(* Basic_1: removed theorems 25:
subst0_gen_sort subst0_gen_lref subst0_gen_head subst0_gen_lift_lt
subst0_gen_lift_false subst0_gen_lift_ge subst0_refl subst0_trans