matita/matita/contribs/lambdadelta/basic_2/etc/csup/csups_csups.etc

   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 "basic_2/substitution/csup_csup.ma".
  16 include "basic_2/unfold/csups.ma".
  17
  18 (* STAR-ITERATED SUPCLOSURE *************************************************)
  19
  20 (* Advanced forward lemmas **************************************************)
  21
  22 (*
  23 lemma csupp_strap2_fwd_refl: ∀L,L0,T1,T2. ⦃L, T1⦄ > ⦃L0, T2⦄ →
  24                              ∀T3. ⦃L0, T2⦄ >+ ⦃L, T3⦄ →
  25                              L = L0 ∨ ⦃L, T1⦄ >+ ⦃L, T3⦄.
  26 #L #L0 #T1 #T2 * -L -L0 -T1 -T2 /2 width=1/
  27 [ #I #L0 #K0 #V0 #i #HLK0 #T3 #H
  28   lapply (ldrop_pair2_fwd_cw … HLK0 T3) -HLK0 #H1
  29   lapply (csupp_fwd_cw … H) -H #H2
  30   lapply (transitive_lt … H1 H2) -H1 -H2 #H
  31   elim (lt_refl_false … H)
  32 | #a #I #L0 #V2 #T2 #T3 #HT23
  33   /3 width=5/
  34
  35   elim (csup_inv_ldrop … HT23 I V2 0 ?) -HT23 // #H1 #H2 destruct /2 width=1/
  36   qed-.
  37
  38
  39
  40
  41
  42
  43
  44
  45 lemma csups_strap1_fwd_refl: ∀L,L0,T1,T2. ⦃L, T1⦄ >* ⦃L0, T2⦄ →
  46                              ∀T3. ⦃L0, T2⦄ > ⦃L, T3⦄ → L = L0.
  47 #L #L0 #T1 #T2 #H @(csups_ind_dx … H) -L -T1 //
  48 #L1 #L #T1 #T #HL1 #_ #IHL0 #T3 #HL0
  49 lapply (csup_trans_fwd_refl … HL10) … HL0) -T2
  50 *)
  51 lemma lift_csups_trans_aux: ∀T1,U1,d,e. ⇧[d, e] T1 ≡ U1 →
  52                             ∀L1,L2,U2. ⦃L1, U1⦄ >* ⦃L2, U2⦄ → L1 = L2 →
  53                             ∃T2. ⇧[d, e] T2 ≡ U2.
  54 #T1 #U1 #d #e #HTU1 #L1 #L2 #U2 #H @(csups_ind … H) -L2 -U2 /2 width=2/ -T1
  55 #L #L2 #U #U2 #HL1 #HL2 #IHL1 #H destruct
  56
  57 * -T1 -U1 -d -e