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15 include "static_2/relocation/lifts_teqg.ma".
16 include "basic_2/rt_transition/cpr_drops_basic.ma".
18 (* CONTEXT-SENSITIVE PARALLEL R-TRANSITION FOR TERMS ************************)
20 (* Properties with context-free generic equivalence *************************)
22 lemma cpr_abbr_pos_tneqx (S) (h) (G) (L) (V) (T1):
23 symmetric … S → (∀s1,s2. Decidable (S s1 s2)) →
24 ∃∃T2. ❪G,L❫ ⊢ +ⓓV.T1 ➡[h,0] T2 & (+ⓓV.T1 ≛[S] T2 → ⊥).
25 #S #h #G #L #V #U1 #H1S #H2S
26 elim (cpr_subst h G (L.ⓓV) U1 … 0) [|*: /2 width=4 by drops_refl/ ] #U2 #T2 #HU12 #HTU2
27 elim (teqg_dec … H2S U1 U2) [ -HU12 #HU12 | -HTU2 #HnU12 ]
28 [ elim (teqg_inv_lifts_dx … HU12 … HTU2) -U2 // #T1 #HTU1 #_ -T2
29 /3 width=9 by cpm_zeta, teqg_lifts_inv_pair_sn, ex2_intro/
30 | @(ex2_intro … (+ⓓV.U2)) [ /2 width=1 by cpm_bind/ ] -HU12 #H
31 elim (teqg_inv_pair … H) -H #_ #_ /2 width=1 by/