+(* Basic_2A1: was: lpxs_inv_atom1 *)
+lemma lpxs_inv_atom_sn (G):
+ ∀L2. ❪G,⋆❫ ⊢ ⬈* L2 → L2 = ⋆.
+/2 width=2 by lex_inv_atom_sn/ qed-.
+
+lemma lpxs_inv_bind_sn (G):
+ ∀I1,L2,K1. ❪G,K1.ⓘ[I1]❫ ⊢ ⬈* L2 →
+ ∃∃I2,K2. ❪G,K1❫ ⊢ ⬈* K2 & ❪G,K1❫ ⊢ I1 ⬈* I2 & L2 = K2.ⓘ[I2].
+/2 width=1 by lex_inv_bind_sn/ qed-.
+
+(* Basic_2A1: was: lpxs_inv_pair1 *)
+lemma lpxs_inv_pair_sn (G):
+ ∀I,L2,K1,V1. ❪G,K1.ⓑ[I]V1❫ ⊢ ⬈* L2 →
+ ∃∃K2,V2. ❪G,K1❫ ⊢ ⬈* K2 & ❪G,K1❫ ⊢ V1 ⬈* V2 & L2 = K2.ⓑ[I]V2.
+/2 width=1 by lex_inv_pair_sn/ qed-.
+
+(* Basic_2A1: was: lpxs_inv_atom2 *)
+lemma lpxs_inv_atom_dx (G):
+ ∀L1. ❪G,L1❫ ⊢ ⬈* ⋆ → L1 = ⋆.
+/2 width=2 by lex_inv_atom_dx/ qed-.
+
+(* Basic_2A1: was: lpxs_inv_pair2 *)
+lemma lpxs_inv_pair_dx (G):
+ ∀I,L1,K2,V2. ❪G,L1❫ ⊢ ⬈* K2.ⓑ[I]V2 →
+ ∃∃K1,V1. ❪G,K1❫ ⊢ ⬈* K2 & ❪G,K1❫ ⊢ V1 ⬈* V2 & L1 = K1.ⓑ[I]V1.
+/2 width=1 by lex_inv_pair_dx/ qed-.