1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/s_computation/fqus_fqup.ma".
16 include "basic_2/static/aaa_drops.ma".
18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
20 (* Properties on supclosure *************************************************)
22 lemma aaa_fqu_conf: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
23 ∀A1. ⦃G1, L1⦄ ⊢ T1 ⁝ A1 → ∃A2. ⦃G2, L2⦄ ⊢ T2 ⁝ A2.
24 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
25 [ #I #G #L #T #A #H elim (aaa_inv_zero … H) -H
26 #J #K #V #H #HA destruct /2 width=2 by ex_intro/
27 | * [ #p ] * #G #L #V #T #X #H
28 [ elim (aaa_inv_abbr … H)
29 | elim (aaa_inv_abst … H)
30 | elim (aaa_inv_appl … H)
31 | elim (aaa_inv_cast … H)
32 ] -H /2 width=2 by ex_intro/
33 | #p * #G #L #V #T #X #H
34 [ elim (aaa_inv_abbr … H)
35 | elim (aaa_inv_abst … H)
36 ] -H /2 width=2 by ex_intro/
38 [ elim (aaa_inv_appl … H)
39 | elim (aaa_inv_cast … H)
40 ] -H /2 width=2 by ex_intro/
41 | /5 width=8 by aaa_inv_lifts, drops_refl, drops_drop, ex_intro/
45 lemma aaa_fquq_conf: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
46 ∀A1. ⦃G1, L1⦄ ⊢ T1 ⁝ A1 → ∃A2. ⦃G2, L2⦄ ⊢ T2 ⁝ A2.
47 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H /2 width=6 by aaa_fqu_conf/
48 * #H1 #H2 #H3 destruct /2 width=2 by ex_intro/
51 lemma aaa_fqup_conf: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
52 ∀A1. ⦃G1, L1⦄ ⊢ T1 ⁝ A1 → ∃A2. ⦃G2, L2⦄ ⊢ T2 ⁝ A2.
53 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
54 [2: #G #G2 #L #L2 #T #T2 #_ #H2 #IH1 #A #HA elim (IH1 … HA) -IH1 -A ]
55 /2 width=6 by aaa_fqu_conf/
58 lemma aaa_fqus_conf: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
59 ∀A1. ⦃G1, L1⦄ ⊢ T1 ⁝ A1 → ∃A2. ⦃G2, L2⦄ ⊢ T2 ⁝ A2.
60 #G1 #G2 #L1 #L2 #T1 #T2 #H elim(fqus_inv_fqup … H) -H /2 width=6 by aaa_fqup_conf/
61 * #H1 #H2 #H3 destruct /2 width=2 by ex_intro/