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 *)
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15 include "basic_2/rt_computation/cpmuwe_cpmuwe.ma".
16 include "basic_2/rt_conversion/cpce_drops.ma".
17 include "basic_2/dynamic/cnv_cpmuwe.ma".
19 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
21 (* Properties with context-sensitive parallel eta-conversion for terms ******)
23 lemma cpce_total_cnv (h) (a) (G) (L):
24 ∀T1. ⦃G,L⦄ ⊢ T1 ![h,a] → ∃T2. ⦃G,L⦄ ⊢ T1 ⬌η[h] T2.
26 lapply (cnv_fwd_csx … HT1) #H
27 generalize in match HT1; -HT1
28 @(csx_ind_fpbg … H) -G -L -T1
30 [ #s #_ #_ /2 width=2 by cpce_sort, ex_intro/
32 elim (drops_ldec_dec L i) [ * #K #W #HLK | -H1i -IH #HnX ]
33 [ lapply (cnv_inv_lref_pair … H2i … HLK) -H2i #H2W
34 lapply (csx_inv_lref_pair_drops … HLK H1i) -H1i #H1W
35 elim (cpmuwe_total_csx … H1W) -H1W #X #n #HWX
36 elim (abst_dec X) [ * | -IH ]
37 [ #p #V1 #U #H destruct
38 lapply (cpmuwe_fwd_cpms … HWX) -HWX #HWX
41 elim (lifts_total V2 (𝐔❴↑i❵)) #W2 #HVW2
42 /3 width=12 by cpce_eta_drops, ex_intro/
43 | /3 width=6 by cnv_cpms_trans, cnv_fwd_pair_sn/
44 | /4 width=6 by fqup_cpms_fwd_fpbg, fpbg_fqu_trans, fqup_lref/
48 @cpce_zero_drops #n0 #p #K0 #W0 #V0 #U0 #HLK0 #HWU0
49 lapply (drops_mono … HLK0 … HLK) -i -L #H destruct
50 lapply (cpmuwe_abst … HWU0) -HWU0 #HWU0
51 elim (cnv_cpmuwe_mono … H2W … HWU0 … HWX) #_ #H -a -n -n0 -W
52 elim (tweq_inv_abst_sn … H) -V0 -U0 #V0 #U0 #H destruct
55 | /5 width=3 by cpce_zero_drops, ex1_2_intro, ex_intro/
57 | #l #_ #_ /2 width=2 by cpce_gref, ex_intro/
58 | #p #I #V1 #T1 #_ #IH #H
59 elim (cnv_inv_bind … H) -H #HV1 #HT1
60 elim (IH … HV1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_pair_sn/ ] #V2 #HV12
61 elim (IH … HT1) [| /4 width=1 by fpb_fpbg, fpb_fqu, fqu_bind_dx/ ] #T2 #HT12
62 /3 width=2 by cpce_bind, ex_intro/
63 | #I #V1 #T1 #_ #IH #H
64 elim (cnv_fwd_flat … H) -H #HV1 #HT1
65 elim (IH … HV1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_pair_sn/ ] #V2 #HV12
66 elim (IH … HT1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_flat_dx/ ] #T2 #HT12
67 /3 width=2 by cpce_flat, ex_intro/