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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 *)
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15 include "basic_2/rt_conversion/cpce_drops.ma".
16 include "basic_2/dynamic/cnv_cpmhe.ma".
18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
20 (* Properties with context-sensitive parallel eta-conversion for terms ******)
22 lemma cpce_total_cnv (a) (h) (G) (L):
23 ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] → ∃T2. ⦃G,L⦄ ⊢ T1 ⬌η[h] T2.
25 lapply (cnv_fwd_csx … HT1) #H
26 generalize in match HT1; -HT1
27 @(csx_ind_fpbg … H) -G -L -T1
29 [ #s #_ #_ /2 width=2 by cpce_sort, ex_intro/
31 elim (drops_ldec_dec L i) [ * #K #W #HLK | -H1i -IH #HnX ]
32 [ lapply (cnv_inv_lref_pair … H2i … HLK) -H2i #H2W
33 lapply (csx_inv_lref_pair_drops … HLK H1i) -H1i #H1W
34 elim (cpmhe_total_csx … H1W) -H1W #X #n #HWX
35 elim (abst_dec X) [ * | -IH ]
36 [ #p #V1 #U #H destruct
37 lapply (cpmhe_fwd_cpms … HWX) -HWX #HWX
40 elim (lifts_total V2 (𝐔❴↑i❵)) #W2 #HVW2
41 /3 width=12 by cpce_eta_drops, ex_intro/
42 | /3 width=6 by cnv_cpms_trans, cnv_fwd_pair_sn/
43 | /4 width=6 by fqup_cpms_fwd_fpbg, fpbg_fqu_trans, fqup_lref/
47 @cpce_zero_drops #n0 #p #K0 #W0 #V0 #U0 #HLK0 #HWU0
48 lapply (drops_mono … HLK0 … HLK) -i -L #H destruct
49 lapply (cpmhe_abst … HWU0) -HWU0 #HWU0
50 elim (cnv_cpmhe_mono … H2W … HWU0 … HWX) #_ #H -a -n -n0 -W
51 elim (theq_inv_pair1 … H) -V0 -U0 #V0 #U0 #H destruct
54 | /5 width=3 by cpce_zero_drops, ex1_2_intro, ex_intro/
56 | #l #_ #_ /2 width=2 by cpce_gref, ex_intro/
57 | #p #I #V1 #T1 #_ #IH #H
58 elim (cnv_inv_bind … H) -H #HV1 #HT1
59 elim (IH … HV1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_pair_sn/ ] #V2 #HV12
60 elim (IH … HT1) [| /4 width=1 by fpb_fpbg, fpb_fqu, fqu_bind_dx/ ] #T2 #HT12
61 /3 width=2 by cpce_bind, ex_intro/
62 | #I #V1 #T1 #_ #IH #H
63 elim (cnv_fwd_flat … H) -H #HV1 #HT1
64 elim (IH … HV1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_pair_sn/ ] #V2 #HV12
65 elim (IH … HT1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_flat_dx/ ] #T2 #HT12
66 /3 width=2 by cpce_flat, ex_intro/