matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu_weight.ma

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   3 (*      ||M||                                                             *)
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  14
  15 include "basic_2/grammar/cl_weight.ma".
  16 include "basic_2/relocation/lifts_weight.ma".
  17 include "basic_2/s_transition/fqu.ma".
  18
  19 (* SUPCLOSURE ***************************************************************)
  20
  21 (* Forward lemmas with weight for closures **********************************)
  22
  23 lemma fqu_fwd_fw: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} < ♯{G1, L1, T1}.
  24 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
  25 #I #I1 #I2 #G #L #V #HI12 normalize in ⊢ (?%%); -I
  26 <(lifts_fwd_tw … HI12) -I1 /3 width=1 by monotonic_lt_plus_r, monotonic_lt_plus_l/
  27 qed-.
  28
  29 (* Advanced eliminators *****************************************************)
  30
  31 lemma fqu_wf_ind: ∀R:relation3 …. (
  32                      ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  33                                  R G1 L1 T1
  34                               ) → ∀G1,L1,T1. R G1 L1 T1.
  35 #R #HR @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct /4 width=1 by fqu_fwd_fw/
  36 qed-.