+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/rt_transition/cpm_cpx.ma".
-include "basic_2/rt_transition/cnh_tdeq.ma".
-include "basic_2/rt_computation/csx.ma".
-include "basic_2/rt_computation/cpmhe.ma".
-
-(* HEAD T-UNBOUND EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS *************)
-
-(* Properties with strong normalization for unbound rt-transition for terms *)
-
-lemma cpmhe_total_csx (h) (G) (L):
- ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∃∃T2,n. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄.
-#h #G #L #T1 #H
-@(csx_ind … H) -T1 #T1 #_ #IHT1
-elim (cnh_dec_tdeq h G L T1)
-[ -IHT1 #HT1 /3 width=4 by cpmhe_intro, ex1_2_intro/
-| * #n1 #T0 #HT10 #HnT10
- elim (IHT1 … HnT10) -IHT1 -HnT10 [| /2 width=2 by cpm_fwd_cpx/ ]
- #T2 #n2 * #HT02 #HT2 /4 width=5 by cpms_step_sn, cpmhe_intro, ex1_2_intro/
-]
-qed-.
-
-lemma R_cpmhe_total_csx (h) (G) (L):
- ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∃n. R_cpmhe h G L T1 n.
-#h #G #L #T1 #H
-elim (cpmhe_total_csx … H) -H #T2 #n #HT12
-/3 width=3 by ex_intro (* 2x *)/
-qed-.