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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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11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/dynamic/cnv_cpm_trans.ma".
16 include "basic_2/dynamic/cnv_cpm_conf.ma".
18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
20 (* Far confluence propery with t-bound rt-computation for terms *************)
22 fact cnv_cpsms_conf_lpr_aux (a) (h) (o):
24 (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) →
25 (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
26 ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpsms_conf_lpr a h o G1 L1 T1.
27 #a #h #o #G #L #T #IH2 #IH1 #G0 #L0 #T0 #HG #HL #HT #HT0
28 #n1 #T1 * #m11 #m12 #X1 #HnX01 #HX01 #HXT1 #H1
29 #n2 #T2 * #m21 #m22 #X2 #HnX02 #HX02 #HXT2 #H2
30 #L1 #HL01 #L2 #HL02 destruct
31 lapply (cnv_cpm_trans_lpr_aux … IH1 IH2 … HX01 … L0 ?) // #HX1
32 lapply (cnv_cpm_trans_lpr_aux … IH1 IH2 … HX02 … L0 ?) // #HX2
33 elim (cnv_cpm_conf_lpr_aux … IH2 IH1 … HX01 … HX02 … L0 … L0) // #Z0 #HXZ10 #HXZ20
34 cut (⦃G0,L0,T0⦄ >[h,o] ⦃G0,L0,X1⦄) [ /4 width=5 by cpms_fwd_fpbs, cpm_fpb, ex2_3_intro/ ] #H1fpbg (**) (* cut *)
35 lapply (fpbg_fpbs_trans ??? G0 ? L0 ? Z0 ? … H1fpbg) [ /2 width=2 by cpms_fwd_fpbs/ ] #H2fpbg
36 lapply (cnv_cpms_trans_lpr_far … IH2 … HXZ10 … L0 ?) // #HZ0
37 elim (IH1 … HXT1 … HXZ10 … L1 … L0) [|*: /4 width=2 by fpb_fpbg, cpm_fpb/ ] -HXT1 -HXZ10 #Z1 #HTZ1 #HZ01
38 elim (IH1 … HXT2 … HXZ20 … L2 … L0) [|*: /4 width=2 by fpb_fpbg, cpm_fpb/ ] -HXT2 -HXZ20 #Z2 #HTZ2 #HZ02
39 elim (IH1 … HZ01 … HZ02 L1 … L2) // -L0 -T0 -X1 -X2 -Z0 #Z #HZ01 #HZ02
40 lapply (cpms_trans … HTZ1 … HZ01) -Z1 <arith_l4 #HT1Z
41 lapply (cpms_trans … HTZ2 … HZ02) -Z2 <arith_l4 #HT2Z
42 /2 width=3 by ex2_intro/