(* *)
(**************************************************************************)
-include "Basic_2/unfold/ltpss_ltpss.ma".
+include "Basic_2/unfold/ltpss_tpss.ma".
include "Basic_2/reducibility/cpr.ma".
(* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
-(* Advanced inversion lemmas ************************************************)
-
-(* Basic_1: was pr2_gen_abbr *)
-lemma cpr_inv_abbr1: ∀L,V1,T1,U2. L ⊢ ⓓV1. T1 ➡ U2 →
- (∃∃V2,T2,T. L ⊢ V1 ➡ V2 & L. ⓓV2 ⊢ T1 ➡ T2 &
- L. ⓓV2 ⊢ T [1, |L|] ▶* T2 &
- U2 = ⓓV2. T
- ) ∨
- ∃∃T. ⇧[0,1] T ≡ T1 & L ⊢ T ➡ U2.
-#L #V1 #T1 #Y * #X #H1 #H2
-elim (tpr_inv_abbr1 … H1) -H1 *
-[ #V #T0 #T #HV1 #HT10 #HT0 #H destruct
- elim (tpss_inv_bind1 … H2) -H2 #V2 #T2 #HV2 #HT2 #H destruct
- lapply (tps_lsubs_conf … HT0 (L. ⓓV) ?) -HT0 /2 width=1/ #HT0
- elim (ltpss_tps_conf … HT0 (L. ⓓV2) 1 (|L|) ?) -HT0 /2 width=1/ #V0 #HV20 #HV0
- lapply (tpss_weak_all … HV20) -HV20 #HV20
- lapply (tpss_lsubs_conf … HV0 (L. ⓓV2) ?) -HV0 /2 width=1/ #HV0
- elim (tpss_conf_eq … HT2 … HV0) -T #T3 #HT23 #HVT3
- lapply (tpss_weak_all … HVT3) -HVT3 #HVT3
- lapply (tpss_trans_eq … HV20 … HVT3) -V0 /4 width=7/
-| /4 width=5/
-]
-qed-.
-
(* Properties concerning partial unfold on local environments ***************)
lemma ltpss_cpr_trans: ∀L1,L2,d,e. L1 [d, e] ▶* L2 →