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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 "static_2/static/aaa_drops.ma".
16 include "static_2/static/lsuba_aaa.ma".
17 include "basic_2/rt_transition/lpx_drops.ma".
19 (* EXTENDED 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 (G) (L1):
26 ∀T1,A. ❨G,L1❩ ⊢ T1 ⁝ A →
27 ∀T2. ❨G,L1❩ ⊢ T1 ⬈ T2 →
28 ∀L2. ❨G,L1❩ ⊢ ⬈ L2 → ❨G,L2❩ ⊢ T2 ⁝ A.
29 #G #L1 #T1 #A #H elim H -G -L1 -T1 -A
31 elim (cpx_inv_sort1 … H) -H #s2 #H destruct //
32 | #I #G #K1 #V1 #B #_ #IH #X #HX #Y #HY
33 elim (lpx_inv_pair_sn … HY) -HY #K2 #V2 #HK12 #HV12 #H destruct
34 elim (cpx_inv_zero1_pair … HX) -HX
35 [ #H destruct /3 width=1 by aaa_zero/
36 | * #V #HV1 #HVX -HV12
37 /4 width=7 by aaa_lifts, drops_refl, drops_drop, true/
39 | #I1 #G #K1 #A #i #_ #IH #X #HX #Y #HY
40 elim (lpx_inv_bind_sn … HY) -HY #I2 #K2 #HK12 #_ #H destruct
41 elim (cpx_inv_lref1_bind … HX) -HX
42 [ #H destruct /3 width=1 by aaa_lref/
44 /4 width=7 by aaa_lifts, drops_refl, drops_drop, true/
46 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
47 elim (cpx_inv_abbr1 … H) -H *
48 [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=2 by lpx_pair, aaa_abbr/
49 | #X1 #HXT1 #HX1 #H destruct -IHV1
50 elim (cpx_lifts_sn … HX1 (Ⓣ) … (L1.ⓓV1) … HXT1) -X1
51 /4 width=7 by lpx_pair, aaa_inv_lifts, drops_refl, drops_drop/
53 | #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
54 elim (cpx_inv_abst1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
55 /4 width=1 by lpx_pair, aaa_abst/
56 | #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
57 elim (cpx_inv_appl1 … H) -H *
58 [ #V2 #T2 #HV12 #HT12 #H destruct /3 width=3 by aaa_appl/
59 | #q #V2 #W1 #W2 #U1 #U2 #HV12 #HW12 #HU12 #H1 #H2 destruct
60 lapply (IHV1 … HV12 … HL12) -IHV1 -HV12 #HV2
61 lapply (IHT1 (ⓛ[q]W2.U2) … HL12) -IHT1 /2 width=1 by cpx_bind/ -L1 #H
62 elim (aaa_inv_abst … H) -H #B0 #A0 #HW1 #HU2 #H destruct
63 /5 width=6 by lsuba_aaa_trans, lsuba_beta, aaa_abbr, aaa_cast/
64 | #q #V #V2 #W1 #W2 #U1 #U2 #HV1 #HV2 #HW12 #HU12 #H1 #H2 destruct
65 lapply (aaa_lifts G L2 … B … (L2.ⓓW2) … HV2) -HV2 /3 width=2 by drops_refl, drops_drop/ #HV2
66 lapply (IHT1 (ⓓ[q]W2.U2) … HL12) -IHT1 /2 width=1 by cpx_bind/ -L1 #H
67 elim (aaa_inv_abbr … H) -H /3 width=3 by aaa_abbr, aaa_appl/
69 | #G #L1 #V1 #T1 #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
70 elim (cpx_inv_cast1 … H) -H
71 [ * #V2 #T2 #HV12 #HT12 #H destruct /3 width=1 by aaa_cast/
72 | -IHV1 /2 width=1 by/
73 | -IHT1 /2 width=1 by/
78 lemma cpx_aaa_conf (G) (L): Conf3 … (aaa G L) (cpx G L).
79 /2 width=7 by cpx_aaa_conf_lpx/ qed-.
81 lemma lpx_aaa_conf (G):
82 ∀T. Conf3 … (λL. aaa G L T) (lpx G).
83 /2 width=7 by cpx_aaa_conf_lpx/ qed-.