matita/matita/contribs/lambdadelta/static_2/relocation/lifts_teqw.ma

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   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "static_2/syntax/teqw.ma".
  16 include "static_2/relocation/lifts_lifts.ma".
  17
  18 (* GENERIC RELOCATION FOR TERMS *********************************************)
  19
  20 (* Properties with sort-irrelevant whd equivalence for terms ****************)
  21
  22 lemma teqw_lifts_sn: liftable2_sn teqw.
  23 #T1 #T2 #H elim H -T1 -T2
  24 [ #s1 #s2 #f #X #H >(lifts_inv_sort1 … H) -H
  25   /3 width=3 by lifts_sort, teqw_sort, ex2_intro/
  26 | #i #f #X #H elim (lifts_inv_lref1 … H) -H
  27   /3 width=3 by lifts_lref, teqw_lref, ex2_intro/
  28 | #l #f #X #H >(lifts_inv_gref1 … H) -H
  29   /2 width=3 by lifts_gref, teqw_gref, ex2_intro/
  30 | #p #V1 #V2 #T1 #T2 #_ #IHT #f #X #H
  31   elim (lifts_inv_bind1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
  32   elim (lifts_total V2 f) #W2 #HVW2
  33   elim (true_or_false p) #H destruct
  34   [ elim (IHT … HTU1) -T1 [| // ] #U2 #HTU2 #HU12
  35   | elim (lifts_total T2 (⫯f)) #U2 #HTU2
  36   ]
  37   /3 width=4 by teqw_abbr_pos, lifts_bind, ex2_intro/
  38 | #p #V1 #V2 #T1 #T2 #f #X #H
  39   elim (lifts_inv_bind1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
  40   elim (lifts_total V2 f) #W2 #HVW2
  41   elim (lifts_total T2 (⫯f)) #U2 #HTU2
  42   /3 width=3 by lifts_bind, ex2_intro/
  43 | #V1 #V2 #T1 #T2 #_ #IHT #f #X #H
  44   elim (lifts_inv_flat1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
  45   elim (lifts_total V2 f) #W2 #HVW2
  46   elim (IHT … HTU1) -T1 #U2 #HTU2 #HU12
  47   /3 width=4 by lifts_flat, teqw_appl, ex2_intro/
  48 | #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f #X #H
  49   elim (lifts_inv_flat1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
  50   elim (IHV … HVW1) -V1 #W2 #HVW2 #HW12
  51   elim (IHT … HTU1) -T1 #U2 #HTU2 #HU12
  52   /3 width=5 by lifts_flat, teqw_cast, ex2_intro/
  53 ]
  54 qed-.
  55
  56 lemma teqw_lifts_dx: liftable2_dx teqw.
  57 /3 width=3 by teqw_lifts_sn, liftable2_sn_dx, teqw_sym/ qed-.
  58
  59 lemma teqw_lifts_bi: liftable2_bi teqw.
  60 /3 width=6 by teqw_lifts_sn, liftable2_sn_bi/ qed-.
  61
  62 (* Inversion lemmas with sort-irrelevant whd equivalence for terms **********)
  63
  64 lemma teqw_inv_lifts_bi: deliftable2_bi teqw.
  65 #U1 #U2 #H elim H -U1 -U2
  66 [ #s1 #s2 #f #X1 #H1 #X2 #H2
  67   >(lifts_inv_sort2 … H1) -H1 >(lifts_inv_sort2 … H2) -H2
  68   /1 width=1 by teqw_sort/
  69 | #j #f #X1 #H1 #X2 #H2
  70   elim (lifts_inv_lref2 … H1) -H1 #i1 #Hj1 #H destruct
  71   elim (lifts_inv_lref2 … H2) -H2 #i2 #Hj2 #H destruct
  72   <(at_inj … Hj2 … Hj1) -j -f -i1
  73   /1 width=1 by teqw_lref/
  74 | #l #f #X1 #H1 #X2 #H2
  75   >(lifts_inv_gref2 … H1) -H1 >(lifts_inv_gref2 … H2) -H2
  76   /1 width=1 by teqw_gref/
  77 | #p #W1 #W2 #U1 #U2 #_ #IH #f #X1 #H1 #X2 #H2
  78   elim (lifts_inv_bind2 … H1) -H1 #V1 #T1 #_ #HTU1 #H destruct -W1
  79   elim (lifts_inv_bind2 … H2) -H2 #V2 #T2 #_ #HTU2 #H destruct -W2
  80   elim (true_or_false p) #H destruct
  81   [ /3 width=3 by teqw_abbr_pos/
  82   | /1 width=1 by teqw_abbr_neg/
  83   ]
  84 | #p #W1 #W2 #U1 #U2 #f #X1 #H1 #X2 #H2
  85   elim (lifts_inv_bind2 … H1) -H1 #V1 #T1 #_ #_ #H destruct -W1 -U1
  86   elim (lifts_inv_bind2 … H2) -H2 #V2 #T2 #_ #_ #H destruct -W2 -U2
  87   /1 width=1 by teqw_abst/
  88 | #W1 #W2 #U1 #U2 #_ #IH #f #X1 #H1 #X2 #H2
  89   elim (lifts_inv_flat2 … H1) -H1 #V1 #T1 #_ #HTU1 #H destruct -W1
  90   elim (lifts_inv_flat2 … H2) -H2 #V2 #T2 #_ #HTU2 #H destruct -W2
  91   /3 width=3 by teqw_appl/
  92 | #W1 #W2 #U1 #U2 #_ #_ #IHW #IHU #f #X1 #H1 #X2 #H2
  93   elim (lifts_inv_flat2 … H1) -H1 #V1 #T1 #HVW1 #HTU1 #H destruct
  94   elim (lifts_inv_flat2 … H2) -H2 #V2 #T2 #HVW2 #HTU2 #H destruct
  95   /3 width=3 by teqw_cast/
  96 ]
  97 qed-.
  98
  99 lemma teqw_inv_abbr_pos_x_lifts_y_y (T) (f):
 100       ∀V,U. +ⓓV.U ≃ T → ⇧*[f]T ≘ U → ⊥.
 101 @(f_ind … tw) #n #IH #T #Hn #f #V #U #H1 #H2 destruct
 102 elim (teqw_inv_abbr_pos_sn … H1) -H1 #X1 #X2 #HX2 #H destruct -V
 103 elim (lifts_inv_bind1 … H2) -H2 #Y1 #Y2 #_ #HXY2 #H destruct
 104 /2 width=7 by/
 105 qed-.