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4 (* ||A|| A project by Andrea Asperti *)
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15 include "static_2/relocation/lifts_teqx.ma".
16 include "basic_2/rt_transition/cpr_drops_basic.ma".
18 (* CONTEXT-SENSITIVE PARALLEL R-TRANSITION FOR TERMS ************************)
20 (* Properties with context-free sort-irrelevant equivalence *****************)
22 lemma cpr_abbr_pos_tneqx (h) (G) (L) (V) (T1):
23 ∃∃T2. ❪G,L❫ ⊢ +ⓓV.T1 ➡[h,0] T2 & (+ⓓV.T1 ≛ T2 → ⊥).
25 elim (cpr_subst h G (L.ⓓV) U1 … 0) [|*: /2 width=4 by drops_refl/ ] #U2 #T2 #HU12 #HTU2
26 elim (teqx_dec U1 U2) [ -HU12 #HU12 | -HTU2 #HnU12 ]
27 [ elim (teqx_inv_lifts_dx … HU12 … HTU2) -U2 #T1 #HTU1 #_ -T2
28 /3 width=9 by cpm_zeta, teqx_lifts_inv_pair_sn, ex2_intro/
29 | @(ex2_intro … (+ⓓV.U2)) [ /2 width=1 by cpm_bind/ ] -HU12 #H
30 elim (teqx_inv_pair … H) -H #_ #_ /2 width=1 by/