matita/matita/contribs/lambdadelta/static_2/relocation/lifts_tueq.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                  *)
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  13 (**************************************************************************)
  14
  15 include "static_2/syntax/tueq.ma".
  16 include "static_2/relocation/lifts_lifts.ma".
  17
  18 (* GENERIC RELOCATION FOR TERMS *********************************************)
  19
  20 (* Properties with tail sort-irrelevant equivalence for terms ***************)
  21
  22 lemma tueq_lifts_sn: liftable2_sn tueq.
  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, tueq_sort, ex2_intro/
  26 | #i #f #X #H elim (lifts_inv_lref1 … H) -H
  27   /3 width=3 by lifts_lref, tueq_lref, ex2_intro/
  28 | #l #f #X #H >(lifts_inv_gref1 … H) -H
  29   /2 width=3 by lifts_gref, tueq_gref, ex2_intro/
  30 | #p #I #V #T1 #T2 #_ #IHT #f #X #H elim (lifts_inv_bind1 … H) -H
  31   #W1 #U1 #HVW1 #HTU1 #H destruct
  32   elim (IHT … HTU1) -T1
  33   /3 width=3 by lifts_bind, tueq_bind, ex2_intro/
  34 | #V #T1 #T2 #_ #IHT #f #X #H elim (lifts_inv_flat1 … H) -H
  35   #W1 #U1 #HVW1 #HTU1 #H destruct
  36   elim (IHT … HTU1) -T1
  37   /3 width=3 by lifts_flat, tueq_appl, ex2_intro/
  38 | #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f #X #H elim (lifts_inv_flat1 … H) -H
  39   #W1 #U1 #HVW1 #HTU1 #H destruct
  40   elim (IHV … HVW1) -V1 elim (IHT … HTU1) -T1
  41   /3 width=5 by lifts_flat, tueq_cast, ex2_intro/
  42 ]
  43 qed-.
  44
  45 lemma tueq_lifts_dx: liftable2_dx tueq.
  46 /3 width=3 by tueq_lifts_sn, liftable2_sn_dx, tueq_sym/ qed-.
  47
  48 lemma tueq_lifts_bi: liftable2_bi tueq.
  49 /3 width=6 by tueq_lifts_sn, liftable2_sn_bi/ qed-.
  50
  51 (* Inversion lemmas with tail sort-irrelevant equivalence for terms *********)
  52
  53 lemma tueq_inv_lifts_sn: deliftable2_sn tueq.
  54 #U1 #U2 #H elim H -U1 -U2
  55 [ #s1 #s2 #f #X #H >(lifts_inv_sort2 … H) -H
  56   /3 width=3 by lifts_sort, tueq_sort, ex2_intro/
  57 | #i #f #X #H elim (lifts_inv_lref2 … H) -H
  58   /3 width=3 by lifts_lref, tueq_lref, ex2_intro/
  59 | #l #f #X #H >(lifts_inv_gref2 … H) -H
  60   /2 width=3 by lifts_gref, tueq_gref, ex2_intro/
  61 | #p #I #W #U1 #U2 #_ #IHU #f #X #H elim (lifts_inv_bind2 … H) -H
  62   #V1 #T1 #HVW1 #HTU1 #H destruct
  63   elim (IHU … HTU1) -U1
  64   /3 width=3 by lifts_bind, tueq_bind, ex2_intro/
  65 | #W #U1 #U2 #_ #IHU #f #X #H elim (lifts_inv_flat2 … H) -H
  66   #V1 #T1 #HVW1 #HTU1 #H destruct
  67   elim (IHU … HTU1) -U1
  68   /3 width=3 by lifts_flat, tueq_appl, ex2_intro/
  69 | #W1 #W2 #U1 #U2 #_ #_ #IHW #IHU #f #X #H elim (lifts_inv_flat2 … H) -H
  70   #V1 #T1 #HVW1 #HTU1 #H destruct
  71   elim (IHW … HVW1) -W1 elim (IHU … HTU1) -U1
  72   /3 width=5 by lifts_flat, tueq_cast, ex2_intro/
  73 ]
  74 qed-.
  75
  76 lemma tueq_inv_lifts_dx: deliftable2_dx tueq.
  77 /3 width=3 by tueq_inv_lifts_sn, deliftable2_sn_dx, tueq_sym/ qed-.
  78
  79 lemma tueq_inv_lifts_bi: deliftable2_bi tueq.
  80 /3 width=6 by tueq_inv_lifts_sn, deliftable2_sn_bi/ qed-.