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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/rt_transition/cnx_cnx.ma".
16 include "basic_2/rt_computation/cpxs.ma".
18 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
20 (* Properties with normal forms *********************************************)
22 lemma cpxs_cnx (h) (G) (L) (T1):
23 (∀T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → T1 ≛ T2) → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃T1⦄.
24 /3 width=1 by cpx_cpxs/ qed.
26 (* Inversion lemmas with normal terms ***************************************)
28 lemma cpxs_inv_cnx1 (h) (G) (L):
29 ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃T1⦄ → T1 ≛ T2.
30 #h #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
31 /5 width=9 by cnx_tdeq_trans, tdeq_trans/