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

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  14
  15 include "basic_2/notation/relations/suptermstar_6.ma".
  16 include "basic_2/s_transition/fquq.ma".
  17
  18 (* STAR-ITERATED SUPCLOSURE *************************************************)
  19
  20 definition fqus: tri_relation genv lenv term ≝ tri_TC … fquq.
  21
  22 interpretation "star-iterated structural successor (closure)"
  23    'SupTermStar G1 L1 T1 G2 L2 T2 = (fqus G1 L1 T1 G2 L2 T2).
  24
  25 (* Basic eliminators ********************************************************)
  26
  27 lemma fqus_ind: ∀G1,L1,T1. ∀R:relation3 …. R G1 L1 T1 →
  28                 (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐⸮ ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
  29                 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → R G2 L2 T2.
  30 #G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
  31 @(tri_TC_star_ind … IH1 IH2 G2 L2 T2 H) //
  32 qed-.
  33
  34 lemma fqus_ind_dx: ∀G2,L2,T2. ∀R:relation3 …. R G2 L2 T2 →
  35                    (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐* ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
  36                    ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ → R G1 L1 T1.
  37 #G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
  38 @(tri_TC_star_ind_dx … IH1 IH2 G1 L1 T1 H) //
  39 qed-.
  40
  41 (* Basic properties *********************************************************)
  42
  43 lemma fqus_refl: tri_reflexive … fqus.
  44 /2 width=1 by tri_inj/ qed.
  45
  46 lemma fquq_fqus: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄.
  47 /2 width=1 by tri_inj/ qed.
  48
  49 lemma fqus_strap1: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
  50                    ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄.
  51 /2 width=5 by tri_step/ qed-.
  52
  53 lemma fqus_strap2: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐* ⦃G2, L2, T2⦄ →
  54                    ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄.
  55 /2 width=5 by tri_TC_strap/ qed-.
  56
  57 (* Basic_2A1: removed theorems 1: fqus_drop *)