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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 *)
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15 include "basic_2/static/aaa_drops.ma".
16 include "basic_2/static/lsuba_aaa.ma".
17 include "basic_2/rt_transition/lpx_drops.ma".
19 (* UNBOUND PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS ***************)
21 (* Properties with atomic arity assignment for terms ************************)
24 (* Basic_2A1: was: cpx_lpx_aaa_conf *)
25 lemma cpx_aaa_conf_lpx (h): ∀G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A →
26 ∀T2. ⦃G, L1⦄ ⊢ T1 ⬈[h] T2 →
27 ∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → ⦃G, L2⦄ ⊢ T2 ⁝ A.
28 #h #G #L1 #T1 #A #H elim H -G -L1 -T1 -A
30 elim (cpx_inv_sort1 … H) -H #H destruct //
31 | #I #G #K1 #V1 #B #_ #IH #X #HX #Y #HY
32 elim (lpx_inv_pair_sn … HY) -HY #K2 #V2 #HK12 #HV12 #H destruct
33 elim (cpx_inv_zero1_pair … HX) -HX
34 [ #H destruct /3 width=1 by aaa_zero/
35 | * #V #HV1 #HVX -HV12
36 /4 width=7 by aaa_lifts, drops_refl, drops_drop, true/
38 | #I1 #G #K1 #A #i #_ #IH #X #HX #Y #HY
39 elim (lpx_inv_bind_sn … HY) -HY #I2 #K2 #HK12 #_ #H destruct
40 elim (cpx_inv_lref1_bind … HX) -HX
41 [ #H destruct /3 width=1 by aaa_lref/
43 /4 width=7 by aaa_lifts, drops_refl, drops_drop, true/
45 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
46 elim (cpx_inv_abbr1 … H) -H *
47 [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=2 by lpx_pair, aaa_abbr/
48 | #T2 #HT12 #HT2 #H destruct -IHV1
49 /4 width=8 by lpx_pair, aaa_inv_lifts, drops_refl, drops_drop/
51 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
52 elim (cpx_inv_abst1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
53 /4 width=1 by lpx_pair, aaa_abst/
54 | #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
55 elim (cpx_inv_appl1 … H) -H *
56 [ #V2 #T2 #HV12 #HT12 #H destruct /3 width=3 by aaa_appl/
57 | #q #V2 #W1 #W2 #U1 #U2 #HV12 #HW12 #HU12 #H1 #H2 destruct
58 lapply (IHV1 … HV12 … HL12) -IHV1 -HV12 #HV2
59 lapply (IHT1 (ⓛ{q}W2.U2) … HL12) -IHT1 /2 width=1 by cpx_bind/ -L1 #H
60 elim (aaa_inv_abst … H) -H #B0 #A0 #HW1 #HU2 #H destruct
61 /5 width=6 by lsuba_aaa_trans, lsuba_beta, aaa_abbr, aaa_cast/
62 | #q #V #V2 #W1 #W2 #U1 #U2 #HV1 #HV2 #HW12 #HU12 #H1 #H2 destruct
63 lapply (aaa_lifts G L2 … B … (L2.ⓓW2) … HV2) -HV2 /3 width=2 by drops_refl, drops_drop/ #HV2
64 lapply (IHT1 (ⓓ{q}W2.U2) … HL12) -IHT1 /2 width=1 by cpx_bind/ -L1 #H
65 elim (aaa_inv_abbr … H) -H /3 width=3 by aaa_abbr, aaa_appl/
67 | #G #L1 #V1 #T1 #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
68 elim (cpx_inv_cast1 … H) -H
69 [ * #V2 #T2 #HV12 #HT12 #H destruct /3 width=1 by aaa_cast/
70 | -IHV1 /2 width=1 by/
71 | -IHT1 /2 width=1 by/
76 lemma cpx_aaa_conf (h): ∀G,L. Conf3 … (aaa G L) (cpx h G L).
77 /2 width=7 by cpx_aaa_conf_lpx/ qed-.
79 lemma lpx_aaa_conf (h): ∀G,T. Conf3 … (λL. aaa G L T) (lpx h G).
80 /2 width=7 by cpx_aaa_conf_lpx/ qed-.