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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
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15 include "basic_2/unfold/ltpss_sn_ltpss_sn.ma".
16 include "basic_2/reducibility/ltpr_ldrop.ma".
17 include "basic_2/reducibility/cpr.ma".
18 include "basic_2/reducibility/lfpr.ma".
20 (* FOCALIZED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS **********************)
22 (* Advanced properties ******************************************************)
24 lemma lfpr_pair_cpr: ∀L1,L2. ⦃L1⦄ ➡ ⦃L2⦄ → ∀V1,V2. L2 ⊢ V1 ➡ V2 →
25 ∀I. ⦃L1. ⓑ{I} V1⦄ ➡ ⦃L2. ⓑ{I} V2⦄.
26 #L1 #L2 * #L #HL1 #HL2 #V1 #V2 *
27 <(ltpss_sn_fwd_length … HL2) #V #HV1 #HV2 #I
28 lapply (ltpss_sn_tpss_trans_eq … HV2 … HL2) -HV2 #V2
29 @(ex2_intro … (L.ⓑ{I}V)) /2 width=1/ (**) (* explicit constructor *)
32 (* Properties on supclosure *************************************************)
34 lamma fsub_cpr_trans: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ∀U2. L2 ⊢ T2 ➡ U2 →
35 ∃∃L,U1. ⦃L1⦄ ➡ ⦃L⦄ & L ⊢ T1 ➡ U1 & ⦃L, U1⦄ ⊃ ⦃L2, U2⦄.
36 #L1 #L2 #T1 #T2 #HT12 #U2 * #T #H1 #H2
37 elim (fsub_tpr_trans … HT12 … H1) -T2 #L #U #HL1 #HT1U #HUT
38 elim (fsup_tpss_trans_full … HUT … H2) -T -HUT -H2 #L #U #HL1 #HT1U #HUT
45 #H elim H -L1 -L2 -T1 -T2 [1,2,3,4,5: /3 width=5/ ]
46 #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #U2 #HTU2
47 elim (IHT12 … HTU2) -IHT12 -HTU2 #K #T #HK1 #HT1 #HK2
48 elim (lift_total T d e) #U #HTU
49 elim (ldrop_ltpr_trans … HLK1 … HK1) -HLK1 -HK1 #L #HL1 #HLK
50 lapply (tpr_lift … HT1 … HTU1 … HTU) -HT1 -HTU1 /3 width=11/