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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  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/theq.ma".
  16 include "static_2/relocation/lifts_lifts.ma".
  17
  18 (* GENERIC RELOCATION FOR TERMS *********************************************)
  19
  20 (* Properties with tail sort-irrelevant head equivalence for terms **********)
  21
  22 lemma theq_lifts_bi: liftable2_bi theq.
  23 #T1 #T2 #H elim H -T1 -T2 [||| * ]
  24 [ #s1 #s2 #f #X1 #H1 #X2 #H2
  25   >(lifts_inv_sort1 … H1) -H1 >(lifts_inv_sort1 … H2) -H2
  26   /1 width=1 by theq_sort/
  27 | #i #f #X1 #H1 #X2 #H2
  28   elim (lifts_inv_lref1 … H1) -H1 #j1 #Hj1 #H destruct
  29   elim (lifts_inv_lref1 … H2) -H2 #j2 #Hj2 #H destruct
  30   <(at_mono … Hj2 … Hj1) -i -f -j2
  31   /1 width=1 by theq_lref/
  32 | #l #f #X1 #H1 #X2 #H2
  33   >(lifts_inv_gref1 … H1) -H1 >(lifts_inv_gref1 … H2) -H2
  34   /1 width=1 by theq_gref/
  35 | #p #I #V1 #V2 #T1 #T2 #f #X1 #H1 #X2 #H2
  36   elim (lifts_inv_bind1 … H1) -H1 #W1 #U1 #_ #_ #H destruct
  37   elim (lifts_inv_bind1 … H2) -H2 #W2 #U2 #_ #_ #H destruct
  38   /1 width=1 by theq_pair/
  39 | #I #V1 #V2 #T1 #T2 #f #X1 #H1 #X2 #H2
  40   elim (lifts_inv_flat1 … H1) -H1 #W1 #U1 #_ #_ #H destruct
  41   elim (lifts_inv_flat1 … H2) -H2 #W2 #U2 #_ #_ #H destruct
  42   /1 width=1 by theq_pair/
  43 ]
  44 qed-.
  45
  46 (* Inversion lemmas with tail sort-irrelevant head equivalence for terms ****)
  47
  48 lemma theq_inv_lifts_bi: deliftable2_bi theq.
  49 #U1 #U2 #H elim H -U1 -U2 [||| * ]
  50 [ #s1 #s2 #f #X1 #H1 #X2 #H2
  51   >(lifts_inv_sort2 … H1) -H1 >(lifts_inv_sort2 … H2) -H2
  52   /1 width=1 by theq_sort/
  53 | #j #f #X1 #H1 #X2 #H2
  54   elim (lifts_inv_lref2 … H1) -H1 #i1 #Hj1 #H destruct
  55   elim (lifts_inv_lref2 … H2) -H2 #i2 #Hj2 #H destruct
  56   <(at_inj … Hj2 … Hj1) -j -f -i1
  57   /1 width=1 by theq_lref/
  58 | #l #f #X1 #H1 #X2 #H2
  59   >(lifts_inv_gref2 … H1) -H1 >(lifts_inv_gref2 … H2) -H2
  60   /1 width=1 by theq_gref/
  61 | #p #I #W1 #W2 #U1 #U2 #f #X1 #H1 #X2 #H2
  62   elim (lifts_inv_bind2 … H1) -H1 #V1 #T1 #_ #_ #H destruct
  63   elim (lifts_inv_bind2 … H2) -H2 #V2 #T2 #_ #_ #H destruct
  64   /1 width=1 by theq_pair/
  65 | #I #W1 #W2 #U1 #U2 #f #X1 #H1 #X2 #H2
  66   elim (lifts_inv_flat2 … H1) -H1 #V1 #T1 #_ #_ #H destruct
  67   elim (lifts_inv_flat2 … H2) -H2 #V2 #T2 #_ #_ #H destruct
  68   /1 width=1 by theq_pair/
  69 ]
  70 qed-.