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14
15 include "basic_2/reduction/crr_append.ma".
16 include "basic_2/reduction/cir.ma".
17
18 (* IRREDUCIBLE TERMS FOR CONTEXT-SENSITIVE REDUCTION ************************)
19
20 (* Advanved properties ******************************************************)
21
22 lemma cir_labst_last: ∀G,L,T,W. ⦃G, L⦄ ⊢ ➡ 𝐈⦃T⦄  → ⦃G, ⋆.ⓛW @@ L⦄ ⊢ ➡ 𝐈⦃T⦄.
23 /3 width=2 by crr_inv_labst_last/ qed.
24
25 lemma cir_tif: ∀G,T,W. ⦃G, ⋆⦄ ⊢ ➡ 𝐈⦃T⦄ → ⦃G, ⋆.ⓛW⦄ ⊢ ➡ 𝐈⦃T⦄.
26 /3 width=2 by crr_inv_trr/ qed.
27
28 (* Advanced inversion lemmas ************************************************)
29
30 lemma cir_inv_append_sn: ∀G,L,K,T. ⦃G, K @@ L⦄ ⊢ ➡ 𝐈⦃T⦄  → ⦃G, L⦄ ⊢ ➡ 𝐈⦃T⦄.
31 /3 width=1/ qed-.
32
33 lemma cir_inv_tir: ∀G,T,W. ⦃G, ⋆.ⓛW⦄ ⊢ ➡ 𝐈⦃T⦄  → ⦃G, ⋆⦄ ⊢ ➡ 𝐈⦃T⦄.
34 /3 width=1/ qed-.