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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "static_2/syntax/teqw_teqg.ma".
16 include "basic_2/rt_computation/csx_cpxs.ma".
17 include "basic_2/rt_computation/cpms_cpxs.ma".
18 include "basic_2/rt_computation/cnuw_cnuw.ma".
19 include "basic_2/rt_computation/cpmuwe.ma".
21 (* T-UNBOUND WHD EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS **************)
23 (* Properties with strongly normalizing terms for extended rt-transition ****)
25 lemma cpmuwe_total_csx (h) (G) (L):
26 ∀T1. ❨G,L❩ ⊢ ⬈*𝐒 T1 → ∃∃T2,n. ❨G,L❩ ⊢ T1 ➡*𝐍𝐖*[h,n] T2.
28 @(csx_ind_cpxs … H) -T1 #T1 #_ #IHT1
29 elim (cnuw_dec_ex h G L T1)
30 [ -IHT1 #HT1 /3 width=4 by cpmuwe_intro, ex1_2_intro/
31 | * #n1 #T0 #HT10 #HnT10
32 elim (IHT1 … T0) -IHT1
33 [ #T2 #n2 * #HT02 #HT2 /4 width=5 by cpms_trans, cpmuwe_intro, ex1_2_intro/
34 | /3 width=2 by teqg_teqw/
35 | /2 width=3 by cpms_fwd_cpxs/
40 lemma R_cpmuwe_total_csx (h) (G) (L):
41 ∀T1. ❨G,L❩ ⊢ ⬈*𝐒 T1 → ∃n. R_cpmuwe h G L T1 n.
43 elim (cpmuwe_total_csx h … H) -H #T2 #n #HT12
44 /3 width=3 by ex_intro (* 2x *)/