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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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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".
20 (* SUPCLOSURE ***************************************************************)
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
32 "structural successor (closure)"
33 'SupTerm G1 L1 T1 G2 L2 T2 = (fqu G1 L1 T1 G2 L2 T2).
35 (* Basic properties *********************************************************)
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.
40 (* Basic_2A1: removed theorems 3:
41 fqu_drop fqu_drop_lt fqu_lref_S_lt