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15 include "basic_2/reduction/cpx_cix.ma".
16 include "basic_2/reduction/cnx_crx.ma".
18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ********************)
20 (* Main properties on irreducibility ****************************************)
22 theorem cix_cnr: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄.
23 /2 width=6 by cpx_fwd_cix/ qed.
25 (* Main inversion lemmas on irreducibility **********************************)
27 theorem cnr_inv_cix: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐈⦃T⦄.
28 /2 width=7 by cnx_inv_crx/ qed-.