1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/rt_transition/cpx_reqx.ma".
16 include "basic_2/rt_computation/csx_csx.ma".
18 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
20 (* Properties with sort-irrelevant equivalence for local environments *******)
22 (* Basic_2A1: uses: csx_lleq_conf *)
23 lemma csx_reqx_conf (h) (G) (L1):
24 ∀T. ❪G,L1❫ ⊢ ⬈*𝐒[h] T →
25 ∀L2. L1 ≛[T] L2 → ❪G,L2❫ ⊢ ⬈*𝐒[h] T.
27 @(csx_ind … H) -T #T1 #_ #IH #L2 #HL12
28 @csx_intro #T2 #HT12 #HnT12
29 elim (reqx_cpx_trans … HL12 … HT12) -HT12
30 /5 width=5 by cpx_reqx_conf_sn, csx_teqx_trans, teqx_trans/
33 (* Basic_2A1: uses: csx_lleq_trans *)
34 lemma csx_reqx_trans (h) (G) (L2):
35 ∀L1,T. L1 ≛[T] L2 → ❪G,L2❫ ⊢ ⬈*𝐒[h] T → ❪G,L1❫ ⊢ ⬈*𝐒[h] T.
36 /3 width=3 by csx_reqx_conf, reqx_sym/ qed-.