include "basic_2/reduction/crx_append.ma".
include "basic_2/reduction/cix.ma".
-(* CONTEXT-SENSITIVE EXTENDED IRREDUCIBLE TERMS *****************************)
+(* IRREDUCIBLE TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ***************)
(* Advanced inversion lemmas ************************************************)
-lemma cix_inv_append_sn: ∀h,g,L,K,T. ⦃h, K @@ L⦄ ⊢ 𝐈[g]⦃T⦄ → ⦃h, L⦄ ⊢ 𝐈[g]⦃T⦄.
-/3 width=1/ qed-.
+lemma cix_inv_append_sn: ∀h,g,G,L,K,T. ⦃G, K @@ L⦄ ⊢ ➡[h, g] 𝐈⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
+/3 width=1 by crx_append_sn/ qed-.
-lemma cix_inv_tix: ∀h,g,L,T. ⦃h, L⦄ ⊢ 𝐈[g]⦃T⦄ → ⦃h, ⋆⦄ ⊢ 𝐈[g]⦃T⦄.
-/3 width=1/ qed-.
+lemma cix_inv_tix: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃T⦄ → ⦃G, ⋆⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
+/3 width=1 by trx_crx/ qed-.