matita/matita/contribs/lambdadelta/basic_2/etc_2A1/lsubr/cpss_lift.etc

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/relocation/ldrop_ldrop.ma".
  16 include "basic_2/substitution/cpss.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL SUBSTITUTION FOR TERMS ************************)
  19
  20 (* Relocation properties ****************************************************)
  21
  22 (* Basic_1: was only: subst1_lift_lt subst1_lift_ge *)
  23 lemma cpss_lift: l_liftable cpss.
  24 #K #T1 #T2 #H elim H -K -T1 -T2
  25 [ #I #K #L #d #e #_ #U1 #H1 #U2 #H2
  26   >(lift_mono … H1 … H2) -H1 -H2 //
  27 | #K #KV #V #V2 #W2 #i #HKV #HV2 #HVW2 #IHV2 #L #d #e #HLK #U1 #H #U2 #HWU2
  28   elim (lift_inv_lref1 … H) * #Hid #H destruct
  29   [ elim (lift_trans_ge … HVW2 … HWU2) -W2 // <minus_plus #W2 #HVW2 #HWU2
  30     elim (ldrop_trans_le … HLK … HKV) -K /2 width=2/ #X #HLK #H
  31     elim (ldrop_inv_skip2 … H) -H /2 width=1/ -Hid #K #Y #HKV #HVY #H destruct /3 width=8/
  32   | lapply (lift_trans_be … HVW2 … HWU2 ? ?) -W2 // /2 width=1/ >plus_plus_comm_23 #HVU2
  33     lapply (ldrop_trans_ge_comm … HLK … HKV ?) -K // -Hid /3 width=6/
  34   ]
  35 | #a #I #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #d #e #HLK #U1 #H1 #U2 #H2
  36   elim (lift_inv_bind1 … H1) -H1 #VV1 #TT1 #HVV1 #HTT1 #H1 destruct
  37   elim (lift_inv_bind1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct /4 width=5/
  38 | #I #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #d #e #HLK #U1 #H1 #U2 #H2
  39   elim (lift_inv_flat1 … H1) -H1 #VV1 #TT1 #HVV1 #HTT1 #H1 destruct
  40   elim (lift_inv_flat1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct /3 width=6/
  41 ]
  42 qed.
  43
  44 (* Basic_1: was only: subst1_gen_lift_lt subst1_gen_lift_ge *)
  45 lemma cpss_inv_lift1: l_deliftable_sn cpss.
  46 #L #U1 #U2 #H elim H -L -U1 -U2
  47 [ * #L #i #K #d #e #_ #T1 #H
  48   [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3/
  49   | elim (lift_inv_lref2 … H) -H * #Hid #H destruct /3 width=3/
  50   | lapply (lift_inv_gref2 … H) -H #H destruct /2 width=3/
  51   ]
  52 | #L #LV #V #V2 #W2 #i #HLV #HV2 #HVW2 #IHV2 #K #d #e #HLK #T1 #H
  53   elim (lift_inv_lref2 … H) -H * #Hid #H destruct
  54   [ elim (ldrop_conf_lt … HLK … HLV) -L // #L #U #HKL #HLV #HUV
  55     elim (IHV2 … HLV … HUV) -V #U2 #HUV2 #HU2
  56     elim (lift_trans_le … HUV2 … HVW2) -V2 // >minus_plus <plus_minus_m_m // -Hid /3 width=8/
  57   | elim (le_inv_plus_l … Hid) #Hdie #Hei
  58     lapply (ldrop_conf_ge … HLK … HLV ?) -L // #HKLV
  59     elim (lift_split … HVW2 d (i - e + 1)) -HVW2 [4: // |3: /2 width=1/ |2: /3 width=1/ ] -Hid -Hdie
  60     #V1 #HV1 >plus_minus // <minus_minus // /2 width=1/ <minus_n_n <plus_n_O /3 width=8/
  61   ]
  62 | #a #I #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #d #e #HLK #X #H
  63   elim (lift_inv_bind2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
  64   elim (IHV12 … HLK … HWV1) -IHV12 #W2 #HW12 #HWV2
  65   elim (IHU12 … HTU1) -IHU12 -HTU1 /3 width=5/
  66 | #I #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #d #e #HLK #X #H
  67   elim (lift_inv_flat2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
  68   elim (IHV12 … HLK … HWV1) -V1
  69   elim (IHU12 … HLK … HTU1) -U1 -HLK /3 width=5/
  70 ]
  71 qed-.