matita/matita/contribs/lambdadelta/basic_2A/reduction/cnx_cix.ma

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  14
  15 include "basic_2A/reduction/cpx_cix.ma".
  16 include "basic_2A/reduction/cnx_crx.ma".
  17
  18 (* NORMAL TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ********************)
  19
  20 (* Main properties on irreducibility ****************************************)
  21
  22 theorem cix_cnx: ∀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.
  24
  25 (* Main inversion lemmas on irreducibility **********************************)
  26
  27 theorem cnx_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-.