matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr_tpss.ma

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  14
  15 include "Basic_2/unfold/ltpss_ltpss.ma".
  16 include "Basic_2/reducibility/cpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
  19
  20 (* Advanced inversion lemmas ************************************************)
  21
  22 (* Basic_1: was pr2_gen_abbr *)
  23 lemma cpr_inv_abbr1: ∀L,V1,T1,U2. L ⊢ ⓓV1. T1 ➡ U2 →
  24                      (∃∃V2,T2,T. L ⊢ V1 ➡ V2 & L. ⓓV2 ⊢ T1 ➡ T2 &
  25                                  L.  ⓓV2 ⊢ T [1, |L|] ▶* T2 &
  26                                  U2 = ⓓV2. T
  27                       ) ∨
  28                       ∃∃T. ⇧[0,1] T ≡ T1 & L ⊢ T ➡ U2.
  29 #L #V1 #T1 #Y * #X #H1 #H2
  30 elim (tpr_inv_abbr1 … H1) -H1 *
  31 [ #V #T0 #T #HV1 #HT10 #HT0 #H destruct
  32   elim (tpss_inv_bind1 … H2) -H2 #V2 #T2 #HV2 #HT2 #H destruct
  33   lapply (tps_lsubs_conf … HT0 (L. ⓓV) ?) -HT0 /2 width=1/ #HT0
  34   elim (ltpss_tps_conf … HT0 (L. ⓓV2) 1 (|L|) ?) -HT0 /2 width=1/ #V0 #HV20 #HV0
  35   lapply (tpss_weak_all … HV20) -HV20 #HV20
  36   lapply (tpss_lsubs_conf … HV0 (L. ⓓV2) ?) -HV0 /2 width=1/ #HV0
  37   elim (tpss_conf_eq … HT2 … HV0) -T #T3 #HT23 #HVT3
  38   lapply (tpss_weak_all … HVT3) -HVT3 #HVT3
  39   lapply (tpss_trans_eq … HV20 … HVT3) -V0 /4 width=7/
  40 | /4 width=5/
  41 ]
  42 qed-.