matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup_weight.ma

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  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: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
  23                    ♯{G2, L2, T2} < ♯{G1, L1, T1}.
  24 #b #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: ∀b. ∀Q:relation3 …. (
  31                       ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
  32                       Q G1 L1 T1
  33                    ) → ∀G1,L1,T1. Q G1 L1 T1.
  34 #b #Q #HQ @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct
  35 /4 width=2 by fqup_fwd_fw/
  36 qed-.
  37
  38 lemma fqup_wf_ind_eq: ∀b. ∀Q:relation3 …. (
  39                          ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
  40                          ∀G2,L2,T2. G1 = G2 → L1 = L2 → T1 = T2 → Q G2 L2 T2
  41                       ) → ∀G1,L1,T1. Q G1 L1 T1.
  42 #b #Q #HQ @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct
  43 /4 width=7 by fqup_fwd_fw/
  44 qed-.