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/lpx.ma".
16 include "basic_2/rt_computation/cpxs_drops.ma".
17 include "basic_2/rt_computation/cpxs_cpxs.ma".
19 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
21 (* Properties with unbound parallel rt-transition for local environments ****)
23 lemma lpx_cpx_trans: ∀h,G. s_r_transitive … (cpx h G) (λ_.lpx h G).
24 #h #G #L2 #T1 #T2 #H @(cpx_ind … H) -G -L2 -T1 -T2
26 | /3 width=2 by cpx_cpxs, cpx_ess/
27 | #I #G #K2 #V2 #V4 #W4 #_ #IH #HVW4 #L1 #H
28 elim (lpx_inv_pair_dx … H) -H #K1 #V1 #HK12 #HV12 #H destruct
29 /4 width=3 by cpxs_delta, cpxs_strap2/
30 | #I2 #G #K2 #T #U #i #_ #IH #HTU #L1 #H
31 elim (lpx_inv_bind_dx … H) -H #I1 #K1 #HK12 #HI12 #H destruct
32 /4 width=3 by cpxs_lref, cpxs_strap2/
33 |5,10: /4 width=1 by cpxs_beta, cpxs_bind, lpx_bind_refl_dx/
34 |6,8,9: /3 width=1 by cpxs_flat, cpxs_ee, cpxs_eps/
35 | /4 width=3 by cpxs_zeta, lpx_bind_refl_dx/
36 | /4 width=3 by cpxs_theta, cpxs_strap1, lpx_bind_refl_dx/
40 lemma lpx_cpxs_trans: ∀h,G. s_rs_transitive … (cpx h G) (λ_.lpx h G).
41 #h #G @s_r_trans_CTC1 /2 width=3 by lpx_cpx_trans/ (**) (* full auto fails *)