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4 (* ||A|| A project by Andrea Asperti *)
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15 (* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
17 include "basic_2/rt_transition/cnx.ma".
18 include "basic_2/rt_computation/csx.ma".
20 (* Properties with normal terms for uncounted parallel rt-transition ********)
22 (* Basic_1: was just: sn3_nf2 *)
23 lemma cnx_csx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
24 /2 width=1 by NF_to_SN/ qed.
26 (* Advanced properties ******************************************************)
28 lemma csx_sort: ∀h,o,G,L,s. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃⋆s⦄.
29 #h #o #G #L #s elim (deg_total h o s)
30 #d generalize in match s; -s elim d -d
31 [ /3 width=3 by cnx_csx, cnx_sort/
32 | #d #IH #s #Hsd lapply (deg_next_SO … Hsd) -Hsd
33 #Hsd @csx_intro #X #H #HX
34 elim (cpx_inv_sort1 … H) -H #H destruct /2 width=1 by/