matita/matita/contribs/lambdadelta/basic_2A/etc/lsubr/cpqs_lift.etc

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  14
  15 include "basic_2/relocation/ldrop_ldrop.ma".
  16 include "basic_2/unfold/cpqs.ma".
  17
  18 (* CONTEXT-SENSITIVE RESTRICTED PARALLEL COMPUTATION FOR TERMS **************)
  19
  20 (* Relocation properties ****************************************************)
  21
  22 lemma cpqs_lift: l_liftable cpqs.
  23 #K #T1 #T2 #H elim H -K -T1 -T2
  24 [ #I #K #L #d #e #_ #U1 #H1 #U2 #H2
  25   >(lift_mono … H1 … H2) -H1 -H2 //
  26 | #K #KV #V #V2 #W2 #i #HKV #HV2 #HVW2 #IHV2 #L #d #e #HLK #U1 #H #U2 #HWU2
  27   elim (lift_inv_lref1 … H) * #Hid #H destruct
  28   [ elim (lift_trans_ge … HVW2 … HWU2) -W2 // <minus_plus #W2 #HVW2 #HWU2
  29     elim (ldrop_trans_le … HLK … HKV) -K /2 width=2/ #X #HLK #H
  30     elim (ldrop_inv_skip2 … H) -H /2 width=1/ -Hid #K #Y #HKV #HVY #H destruct /3 width=8/
  31   | lapply (lift_trans_be … HVW2 … HWU2 ? ?) -W2 // /2 width=1/ >plus_plus_comm_23 #HVU2
  32     lapply (ldrop_trans_ge_comm … HLK … HKV ?) -K // -Hid /3 width=6/
  33   ]
  34 | #a #I #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #d #e #HLK #U1 #H1 #U2 #H2
  35   elim (lift_inv_bind1 … H1) -H1 #VV1 #TT1 #HVV1 #HTT1 #H1 destruct
  36   elim (lift_inv_bind1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct /4 width=5/
  37 | #I #K #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L #d #e #HLK #U1 #H1 #U2 #H2
  38   elim (lift_inv_flat1 … H1) -H1 #VV1 #TT1 #HVV1 #HTT1 #H1 destruct
  39   elim (lift_inv_flat1 … H2) -H2 #VV2 #TT2 #HVV2 #HTT2 #H2 destruct /3 width=6/
  40 | #K #V #T1 #T #T2 #_ #HT2 #IHT1 #L #d #e #HLK #U1 #H #U2 #HTU2
  41   elim (lift_inv_bind1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct
  42   elim (lift_conf_O1 … HTU2 … HT2) -T2 /4 width=5/
  43 | #K #V #T1 #T2 #_ #IHT12 #L #d #e #HLK #U1 #H #U2 #HTU2
  44   elim (lift_inv_flat1 … H) -H #VV1 #TT1 #HVV1 #HTT1 #H destruct /3 width=5/
  45 ]
  46 qed.
  47
  48 lemma cpqs_inv_lift1: l_deliftable_sn cpqs.
  49 #L #U1 #U2 #H elim H -L -U1 -U2
  50 [ * #L #i #K #d #e #_ #T1 #H
  51   [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3/
  52   | elim (lift_inv_lref2 … H) -H * #Hid #H destruct /3 width=3/
  53   | lapply (lift_inv_gref2 … H) -H #H destruct /2 width=3/
  54   ]
  55 | #L #LV #V #V2 #W2 #i #HLV #HV2 #HVW2 #IHV2 #K #d #e #HLK #T1 #H
  56   elim (lift_inv_lref2 … H) -H * #Hid #H destruct
  57   [ elim (ldrop_conf_lt … HLK … HLV) -L // #L #U #HKL #HLV #HUV
  58     elim (IHV2 … HLV … HUV) -V #U2 #HUV2 #HU2
  59     elim (lift_trans_le … HUV2 … HVW2) -V2 // >minus_plus <plus_minus_m_m // -Hid /3 width=8/
  60   | elim (le_inv_plus_l … Hid) #Hdie #Hei
  61     lapply (ldrop_conf_ge … HLK … HLV ?) -L // #HKLV
  62     elim (lift_split … HVW2 d (i - e + 1)) -HVW2 [4: // |3: /2 width=1/ |2: /3 width=1/ ] -Hid -Hdie
  63     #V1 #HV1 >plus_minus // <minus_minus // /2 width=1/ <minus_n_n <plus_n_O /3 width=8/
  64   ]
  65 | #a #I #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #d #e #HLK #X #H
  66   elim (lift_inv_bind2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
  67   elim (IHV12 … HLK … HWV1) -IHV12 #W2 #HW12 #HWV2
  68   elim (IHU12 … HTU1) -IHU12 -HTU1 /3 width=5/
  69 | #I #L #V1 #V2 #U1 #U2 #_ #_ #IHV12 #IHU12 #K #d #e #HLK #X #H
  70   elim (lift_inv_flat2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
  71   elim (IHV12 … HLK … HWV1) -V1
  72   elim (IHU12 … HLK … HTU1) -U1 -HLK /3 width=5/
  73 | #L #V #U1 #U #U2 #_ #HU2 #IHU1 #K #d #e #HLK #X #H
  74   elim (lift_inv_bind2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
  75   elim (IHU1 (K.ⓓW1) … HTU1) /2 width=1/ -L -U1 #T #HTU #HT1
  76   elim (lift_div_le … HU2 … HTU) -U // /3 width=5/
  77 | #L #V #U1 #U2 #_ #IHU12 #K #d #e #HLK #X #H
  78   elim (lift_inv_flat2 … H) -H #W1 #T1 #HWV1 #HTU1 #H destruct
  79   elim (IHU12 … HLK … HTU1) -L -U1 /3 width=3/
  80 ]
  81 qed-.