matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup_weight.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 "basic_2/s_transition/fqu_weight.ma".
  16 include "basic_2/s_computation/fqup.ma".
  17
  18 (* PLUS-ITERATED SUPCLOSURE *************************************************)
  19
  20 (* Forward lemmas with weight for closures **********************************)
  21
  22 lemma fqup_fwd_fw: ∀G1,G2,L1,L2,T1,T2.
  23                    ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} < ♯{G1, L1, T1}.
  24 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
  25 /3 width=3 by fqu_fwd_fw, transitive_lt/
  26 qed-.
  27
  28 (* Advanced eliminators *****************************************************)
  29
  30 lemma fqup_wf_ind: ∀R:relation3 …. (
  31                       ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  32                       R G1 L1 T1
  33                    ) → ∀G1,L1,T1. R G1 L1 T1.
  34 #R #HR @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct /4 width=1 by fqup_fwd_fw/
  35 qed-.
  36
  37 lemma fqup_wf_ind_eq: ∀R:relation3 …. (
  38                          ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  39                          ∀G2,L2,T2. G1 = G2 → L1 = L2 → T1 = T2 → R G2 L2 T2
  40                       ) → ∀G1,L1,T1. R G1 L1 T1.
  41 #R #HR @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct /4 width=7 by fqup_fwd_fw/
  42 qed-.