matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss_dx.ma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/unfold/tpss_tpss.ma".
  16 include "basic_2/unfold/ltpss_dx_ldrop.ma".
  17 include "basic_2/static/aaa_lift.ma".
  18
  19 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
  20
  21 (* Properties about dx parallel unfold **************************************)
  22
  23 (* Note: lemma 500 *)
  24 lemma aaa_ltpss_dx_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
  25                               ∀L2,d,e. L1 ▶* [d, e] L2 →
  26                               ∀T2. L2 ⊢ T1 ▶* [d, e] T2 → L2 ⊢ T2 ⁝ A.
  27 #L1 #T1 #A #H elim H -L1 -T1 -A
  28 [ #L1 #k #L2 #d #e #_ #T2 #H
  29   >(tpss_inv_sort1 … H) -H //
  30 | #I #L1 #K1 #V1 #B #i #HLK1 #_ #IHV1 #L2 #d #e #HL12 #T2 #H
  31   elim (tpss_inv_lref1 … H) -H
  32   [ #H destruct
  33     elim (lt_or_ge i d) #Hdi
  34     [ elim (ltpss_dx_ldrop_conf_le … HL12 … HLK1 ?) -L1 /2 width=2/ #X #H #HLK2
  35       elim (ltpss_dx_inv_tpss11 … H ?) -H /2 width=1/ -Hdi #K2 #V2 #HK12 #HV12 #H destruct
  36       /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
  37     | elim (lt_or_ge i (d + e)) #Hide
  38       [ elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HLK2
  39         elim (ltpss_dx_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K2 #V2 #HK12 #HV12 #H destruct
  40         /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
  41       | -Hdi
  42         lapply (ltpss_dx_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide
  43         /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
  44       ]
  45     ]
  46   | * #K2 #V2 #W2 #Hdi #Hide #HLK2 #HVW2 #HWT2
  47     elim (ltpss_dx_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HL2K0
  48     elim (ltpss_dx_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K0 #V0 #HK12 #HV12 #H destruct
  49     lapply (ldrop_mono … HL2K0 … HLK2) -HL2K0 #H destruct
  50     lapply (ldrop_fwd_ldrop2 … HLK2) -HLK2 #HLK2
  51     lapply (tpss_trans_eq … HV12 HVW2) -V2 /3 width=7/
  52   ]
  53 | #a #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
  54   elim (tpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=4/
  55 | #a #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
  56   elim (tpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=4/
  57 | #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
  58   elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /3 width=4/
  59 | #L1 #V1 #T1 #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
  60   elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /3 width=4/
  61 ]
  62 qed.
  63
  64 lemma aaa_ltpss_dx_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
  65                              ∀L2,d,e. L1 ▶* [d, e] L2 →
  66                              ∀T2. L2 ⊢ T1 ▶ [d, e] T2 → L2 ⊢ T2 ⁝ A.
  67 /3 width=7/ qed.
  68
  69 lemma aaa_ltpss_dx_conf: ∀L1,T,A. L1 ⊢ T ⁝ A →
  70                          ∀L2,d,e. L1 ▶* [d, e] L2 → L2 ⊢ T ⁝ A.
  71 /2 width=7/ qed.
  72
  73 lemma aaa_tpss_conf: ∀L,T1,A. L ⊢ T1 ⁝ A →
  74                      ∀T2,d,e. L ⊢ T1 ▶* [d, e] T2 → L ⊢ T2 ⁝ A.
  75 /2 width=7/ qed.
  76
  77 lemma aaa_tps_conf: ∀L,T1,A. L ⊢ T1 ⁝ A →
  78                     ∀T2,d,e. L ⊢ T1 ▶ [d, e] T2 → L ⊢ T2 ⁝ A.
  79 /2 width=7/ qed.