(**************************************************************************) (* ___ *) (* ||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 "static_2/relocation/lifts_teqx.ma". include "basic_2/rt_transition/cpr_drops_basic.ma". (* CONTEXT-SENSITIVE PARALLEL R-TRANSITION FOR TERMS ************************) (* Properties with context-free sort-irrelevant equivalence *****************) lemma cpr_abbr_pos_tneqx (h) (G) (L) (V) (T1): ∃∃T2. ❪G,L❫ ⊢ +ⓓV.T1 ➡[h,0] T2 & (+ⓓV.T1 ≛ T2 → ⊥). #h #G #L #V #U1 elim (cpr_subst h G (L.ⓓV) U1 … 0) [|*: /2 width=4 by drops_refl/ ] #U2 #T2 #HU12 #HTU2 elim (teqx_dec U1 U2) [ -HU12 #HU12 | -HTU2 #HnU12 ] [ elim (teqx_inv_lifts_dx … HU12 … HTU2) -U2 #T1 #HTU1 #_ -T2 /3 width=9 by cpm_zeta, teqx_lifts_inv_pair_sn, ex2_intro/ | @(ex2_intro … (+ⓓV.U2)) [ /2 width=1 by cpm_bind/ ] -HU12 #H elim (teqx_inv_pair … H) -H #_ #_ /2 width=1 by/ ] qed-.