matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_weight.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/cl_weight.ma".
  16 include "static_2/relocation/lifts_weight.ma".
  17 include "static_2/s_transition/fqu.ma".
  18
  19 (* SUPCLOSURE ***************************************************************)
  20
  21 (* Forward lemmas with weight for closures **********************************)
  22
  23 lemma fqu_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ →
  24                   ♯❨G2,L2,T2❩ < ♯❨G1,L1,T1❩.
  25 #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
  26 #I #I1 #I2 #G #L #HI12 normalize in ⊢ (?%%); -I1
  27 <(lifts_fwd_tw … HI12) /3 width=1 by nlt_plus_bi_sn, nlt_plus_bi_dx/
  28 qed-.
  29
  30 (* Advanced eliminators *****************************************************)
  31
  32 lemma fqu_wf_ind: ∀b. ∀Q:relation3 …. (
  33                      ∀G1,L1,T1. (∀G2,L2,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ → Q G2 L2 T2) →
  34                                  Q G1 L1 T1
  35                               ) → ∀G1,L1,T1. Q G1 L1 T1.
  36 #b #Q #HQ @(wf3_ind_nlt … fw) #x #IHx #G1 #L1 #T1 #H destruct /4 width=2 by fqu_fwd_fw/
  37 qed-.