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

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  14
  15 include "basic_2/notation/relations/supterm_6.ma".
  16 include "basic_2/grammar/lenv.ma".
  17 include "basic_2/grammar/genv.ma".
  18 include "basic_2/relocation/lifts.ma".
  19
  20 (* SUPCLOSURE ***************************************************************)
  21
  22 (* activate genv *)
  23 inductive fqu: tri_relation genv lenv term ≝
  24 | fqu_lref_O : ∀I,G,L,V. fqu G (L.ⓑ{I}V) (#0) G L V
  25 | fqu_pair_sn: ∀I,G,L,V,T. fqu G L (②{I}V.T) G L V
  26 | fqu_bind_dx: ∀p,I,G,L,V,T. fqu G L (ⓑ{p,I}V.T) G (L.ⓑ{I}V) T
  27 | fqu_flat_dx: ∀I,G,L,V,T. fqu G L (ⓕ{I}V.T) G L T
  28 | fqu_drop   : ∀I,G,L,V,T,U. ⬆*[1] T ≡ U → fqu G (L.ⓑ{I}V) U G L T
  29 .
  30
  31 interpretation
  32    "structural successor (closure)"
  33    'SupTerm G1 L1 T1 G2 L2 T2 = (fqu G1 L1 T1 G2 L2 T2).
  34
  35 (* Basic properties *********************************************************)
  36
  37 lemma fqu_lref_S: ∀I,G,L,V,i. ⦃G, L.ⓑ{I}V, #(⫯i)⦄ ⊐ ⦃G, L, #(i)⦄.
  38 /2 width=1 by fqu_drop/ qed.
  39
  40 (* Basic_2A1: removed theorems 3:
  41               fqu_drop fqu_drop_lt fqu_lref_S_lt
  42 *)