+
+(* Basic_2A1: was: lprs_inv_pair2 *)
+lemma lprs_inv_pair_dx (h) (G):
+ ∀I,L1,K2,V2. ❨G,L1❩ ⊢ ➡*[h,0] K2.ⓑ[I]V2 →
+ ∃∃K1,V1. ❨G,K1❩ ⊢ ➡*[h,0] K2 & ❨G,K1❩ ⊢ V1 ➡*[h,0] V2 & L1 = K1.ⓑ[I]V1.
+/2 width=1 by lex_inv_pair_dx/ qed-.
+
+(* Basic eliminators ********************************************************)
+
+(* Basic_2A1: was: lprs_ind_alt *)
+lemma lprs_ind (h) (G): ∀Q:relation lenv.
+ Q (⋆) (⋆) → (
+ ∀I,K1,K2.
+ ❨G,K1❩ ⊢ ➡*[h,0] K2 →
+ Q K1 K2 → Q (K1.ⓘ[I]) (K2.ⓘ[I])
+ ) → (
+ ∀I,K1,K2,V1,V2.
+ ❨G,K1❩ ⊢ ➡*[h,0] K2 → ❨G,K1❩ ⊢ V1 ➡*[h,0] V2 →
+ Q K1 K2 → Q (K1.ⓑ[I]V1) (K2.ⓑ[I]V2)
+ ) →
+ ∀L1,L2. ❨G,L1❩ ⊢ ➡*[h,0] L2 → Q L1 L2.
+/3 width=4 by lex_ind/ qed-.