matita/matita/contribs/lambda_delta/basic_2/computation/lsubc_ldrop.ma

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  14
  15 include "basic_2/static/aaa_lift.ma".
  16 include "basic_2/computation/lsubc.ma".
  17
  18 (* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
  19
  20 (* Properties concerning basic local environment slicing ********************)
  21
  22 (* Basic_1: was: csubc_drop_conf_O *)
  23 (* Note: the constant 0 can not be generalized *)
  24 lemma lsubc_ldrop_O1_trans: ∀RP,L1,L2. L1 ⊑[RP] L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
  25                             ∃∃K1. ⇩[0, e] L1 ≡ K1 & K1 ⊑[RP] K2.
  26 #RP #L1 #L2 #H elim H -L1 -L2
  27 [ #X #e #H
  28   >(ldrop_inv_atom1 … H) -H /2 width=3/
  29 | #I #L1 #L2 #V #_ #IHL12 #X #e #H
  30   elim (ldrop_inv_O1 … H) -H * #He #H destruct
  31   [ elim (IHL12 L2 0 ?) -IHL12 // #X #H <(ldrop_inv_refl … H) -H /3 width=3/
  32   | elim (IHL12 … H) -L2 /3 width=3/
  33   ]
  34 | #L1 #L2 #V #W #A #HV #HW #_ #IHL12 #X #e #H
  35   elim (ldrop_inv_O1 … H) -H * #He #H destruct
  36   [ elim (IHL12 L2 0 ?) -IHL12 // #X #H <(ldrop_inv_refl … H) -H /3 width=7/
  37   | elim (IHL12 … H) -L2 /3 width=3/
  38   ]
  39 qed-.
  40
  41 (* Basic_1: was: csubc_drop_conf_rev *)
  42 lemma ldrop_lsubc_trans: ∀RR,RS,RP.
  43                          acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
  44                          ∀L1,K1,d,e. ⇩[d, e] L1 ≡ K1 → ∀K2. K1 ⊑[RP] K2 →
  45                          ∃∃L2. L1 ⊑[RP] L2 & ⇩[d, e] L2 ≡ K2.
  46 #RR #RS #RP #Hacp #Hacr #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
  47 [ #d #e #X #H
  48   >(lsubc_inv_atom1 … H) -H /2 width=3/
  49 | #L1 #I #V1 #X #H
  50   elim (lsubc_inv_pair1 … H) -H *
  51   [ #K1 #HLK1 #H destruct /3 width=3/
  52   | #K1 #W1 #A #HV1 #HW1 #HLK1 #H1 #H2 destruct /3 width=3/
  53   ]
  54 | #L1 #K1 #I #V1 #e #_ #IHLK1 #K2 #HK12
  55   elim (IHLK1 … HK12) -K1 /3 width=5/
  56 | #L1 #K1 #I #V1 #V2 #d #e #HLK1 #HV21 #IHLK1 #X #H
  57   elim (lsubc_inv_pair1 … H) -H *
  58   [ #K2 #HK12 #H destruct
  59     elim (IHLK1 … HK12) -K1 /3 width=5/
  60   | #K2 #W2 #A #HV2 #HW2 #HK12 #H1 #H2 destruct
  61     elim (IHLK1 … HK12) #K #HL1K #HK2
  62     lapply (aacr_acr … Hacp Hacr A) -Hacp -Hacr #HA
  63     lapply (s7 … HA … HV2 … HLK1 HV21) -HV2
  64     elim (lift_total W2 d e) /4 width=9/
  65   ]
  66 ]
  67 qed-.