]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/basic_2A/substitution/fquq.ma
update in ground
[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / substitution / fquq.ma
1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 include "basic_2A/notation/relations/suptermopt_6.ma".
16 include "basic_2A/substitution/fqu.ma".
17
18 (* OPTIONAL SUPCLOSURE ******************************************************)
19
20 (* activate genv *)
21 inductive fquq: tri_relation genv lenv term ≝
22 | fquq_lref_O : ∀I,G,L,V. fquq G (L.ⓑ{I}V) (#0) G L V
23 | fquq_pair_sn: ∀I,G,L,V,T. fquq G L (②{I}V.T) G L V
24 | fquq_bind_dx: ∀a,I,G,L,V,T. fquq G L (ⓑ{a,I}V.T) G (L.ⓑ{I}V) T
25 | fquq_flat_dx: ∀I,G, L,V,T. fquq G L (ⓕ{I}V.T) G L T
26 | fquq_drop   : ∀G,L,K,T,U,m.
27                 ⬇[m] L ≡ K → ⬆[0, m] T ≡ U → fquq G L U G K T
28 .
29
30 interpretation
31    "optional structural successor (closure)"
32    'SupTermOpt G1 L1 T1 G2 L2 T2 = (fquq G1 L1 T1 G2 L2 T2).
33
34 (* Basic properties *********************************************************)
35
36 lemma fquq_refl: tri_reflexive … fquq.
37 /2 width=3 by fquq_drop/ qed.
38
39 lemma fqu_fquq: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄.
40 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 /2 width=3 by fquq_drop/
41 qed.
42
43 (* Basic forward lemmas *****************************************************)
44
45 lemma fquq_fwd_fw: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} ≤ ♯{G1, L1, T1}.
46 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 /2 width=1 by lt_to_le/
47 #G1 #L1 #K1 #T1 #U1 #m #HLK1 #HTU1
48 lapply (drop_fwd_lw … HLK1) -HLK1
49 lapply (lift_fwd_tw … HTU1) -HTU1
50 /2 width=1 by le_plus, le_n/
51 qed-.
52
53 fact fquq_fwd_length_lref1_aux: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
54                                 ∀i. T1 = #i → |L2| ≤ |L1|.
55 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
56 [ #a #I #G #L #V #T #j #H destruct
57 | #G1 #L1 #K1 #T1 #U1 #m #HLK1 #HTU1 #i #H destruct
58   /2 width=3 by drop_fwd_length_le4/
59 ]
60 qed-.
61
62 lemma fquq_fwd_length_lref1: ∀G1,G2,L1,L2,T2,i. ⦃G1, L1, #i⦄ ⊐⸮ ⦃G2, L2, T2⦄ → |L2| ≤ |L1|.
63 /2 width=7 by fquq_fwd_length_lref1_aux/
64 qed-.