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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-.