matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc_ldrop.ma

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "Basic_2/static/aaa_lift.ma".
  16 include "Basic_2/computation/acp_cr.ma".
  17 include "Basic_2/computation/lsubc.ma".
  18
  19 (* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
  20
  21 (* Properties concerning basic local environment slicing ********************)
  22
  23 (* Basic_1: was: csubc_drop_conf_O *)
  24 (* Note: the constant (0) can not be generalized *)
  25 lemma lsubc_ldrop_O1_trans: ∀RP,L1,L2. L1 [RP] ⊑ L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
  26                             ∃∃K1. ⇩[0, e] L1 ≡ K1 & K1 [RP] ⊑ K2.
  27 #RP #L1 #L2 #H elim H -L1 -L2
  28 [ #X #e #H
  29   >(ldrop_inv_atom1 … H) -H /2 width=3/
  30 | #I #L1 #L2 #V #_ #IHL12 #X #e #H
  31   elim (ldrop_inv_O1 … H) -H * #He #H destruct
  32   [ elim (IHL12 L2 0 ?) -IHL12 // #X #H <(ldrop_inv_refl … H) -H /3 width=3/
  33   | elim (IHL12 … H) -L2 /3 width=3/
  34   ]
  35 | #L1 #L2 #V #W #A #HV #HW #_ #IHL12 #X #e #H
  36   elim (ldrop_inv_O1 … H) -H * #He #H destruct
  37   [ elim (IHL12 L2 0 ?) -IHL12 // #X #H <(ldrop_inv_refl … H) -H /3 width=7/
  38   | elim (IHL12 … H) -L2 /3 width=3/
  39   ]
  40 qed-.
  41
  42 (* Basic_1: was: csubc_drop_conf_rev *)
  43 lemma ldrop_lsubc_trans: ∀RR,RS,RP.
  44                          acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
  45                          ∀L1,K1,d,e. ⇩[d, e] L1 ≡ K1 → ∀K2. K1 [RP] ⊑ K2 →
  46                          ∃∃L2. L1 [RP] ⊑ L2 & ⇩[d, e] L2 ≡ K2.
  47 #RR #RS #RP #Hacp #Hacr #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
  48 [ #d #e #X #H
  49   >(lsubc_inv_atom1 … H) -H /2 width=3/
  50 | #L1 #I #V1 #X #H
  51   elim (lsubc_inv_pair1 … H) -H *
  52   [ #K1 #HLK1 #H destruct /3 width=3/
  53   | #K1 #W1 #A #HV1 #HW1 #HLK1 #H1 #H2 destruct /3 width=3/
  54   ]
  55 | #L1 #K1 #I #V1 #e #_ #IHLK1 #K2 #HK12
  56   elim (IHLK1 … HK12) -K1 /3 width=5/
  57 | #L1 #K1 #I #V1 #V2 #d #e #HLK1 #HV21 #IHLK1 #X #H
  58   elim (lsubc_inv_pair1 … H) -H *
  59   [ #K2 #HK12 #H destruct
  60     elim (IHLK1 … HK12) -K1 /3 width=5/
  61   | #K2 #W2 #A #HV2 #HW2 #HK12 #H1 #H2 destruct
  62     elim (IHLK1 … HK12) #K #HL1K #HK2
  63     lapply (aacr_acr … Hacp Hacr A) -Hacp -Hacr #HA
  64     lapply (s7 … HA … HV2 … HLK1 HV21) -HV2
  65     elim (lift_total W2 d e) /4 width=9/
  66   ]
  67 ]
  68 qed-.