interpretation
"preterm (prototerm)"
'ClassT = (structure_injective).
+
+(* Basic inversions *********************************************************)
+
+lemma preterm_in_root_append_inv_structure_empty_dx (t) (p) (r):
+ p●r ϵ ▵t → t ϵ 𝐓 → 𝐞 = ⊗r → 𝐞 = r.
+#t #p #r #Hpr #Ht #Hr
+lapply (Ht p ?? Hpr ?)
+[ <structure_append //
+| /2 width=2 by prototerm_in_root_append_des_sn/
+| /2 width=3 by eq_inv_list_append_dx_sn_refl/
+]
+qed-.