(* Basic inversion lemmas ***************************************************)
-(* Basic_1: includes: wcpr0_gen_sort *)
lemma lpr_inv_atom1: ∀G,L2. ⦃G, ⋆⦄ ⊢ ➡ L2 → L2 = ⋆.
/2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
-(* Basic_1: includes: wcpr0_gen_head *)
lemma lpr_inv_pair1: ∀I,G,K1,V1,L2. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ L2 →
∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L2 = K2.ⓑ{I}V2.
/2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
lemma lpr_fwd_length: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → |L1| = |L2|.
/2 width=2 by lpx_sn_fwd_length/ qed-.
-
-(* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back
- pr0_subst1_back
-*)