matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/ltpr_ldrop.etc

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  14
  15 include "basic_2/substitution/ldrop_lpx.ma".
  16 include "basic_2/substitution/fsup.ma".
  17 include "basic_2/reducibility/tpr_lift.ma".
  18 include "basic_2/reducibility/ltpr.ma".
  19
  20 (* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
  21
  22 (* Properies on local environment slicing ***********************************)
  23
  24 (* Basic_1: was: wcpr0_drop *)
  25 lemma ltpr_ldrop_conf: dropable_sn ltpr.
  26 /3 width=3 by lpx_deliftable_dropable, tpr_inv_lift1/ qed.
  27
  28 (* Basic_1: was: wcpr0_drop_back *)
  29 lemma ldrop_ltpr_trans: dedropable_sn ltpr.
  30 /2 width=3/ qed.
  31
  32 lemma ltpr_ldrop_trans_O1: dropable_dx ltpr.
  33 /2 width=3/ qed.
  34
  35 (* Properties on supclosure *************************************************)
  36
  37 lemma fsub_tpr_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ∀U2. T2 ➡ U2 →
  38                       ∃∃L,U1. L1 ➡ L & T1 ➡ U1 & ⦃L, U1⦄ ⊃ ⦃L2, U2⦄.
  39 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 [1,2,3,4,5: /3 width=5/ ]
  40 #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
  41 elim (IHT12 … HTU2) -IHT12 -HTU2 #K #T #HK1 #HT1 #HK2
  42 elim (lift_total T d e) #U #HTU
  43 elim (ldrop_ltpr_trans … HLK1 … HK1) -HLK1 -HK1 #L #HL1 #HLK
  44 lapply (tpr_lift … HT1 … HTU1 … HTU) -HT1 -HTU1 /3 width=11/
  45 qed-.