(* *)
(**************************************************************************)
+include "basic_2/rt_computation/cpmuwe_cpmuwe.ma".
include "basic_2/rt_equivalence/cpes_cpes.ma".
-include "basic_2/dynamic/cnv_cpmhe.ma".
+include "basic_2/dynamic/cnv_cpmuwe.ma". (**) (* should be included by the next *)
+include "basic_2/dynamic/cnv_cpmuwe_cpmre.ma".
include "basic_2/dynamic/cnv_cpes.ma".
include "basic_2/dynamic/cnv_preserve_cpes.ma".
(* main properties with evaluations for rt-transition on terms **************)
-theorem cnv_dec (a) (h) (G) (L) (T): ac_props a →
- Decidable (â¦\83G,Lâ¦\84 â\8a¢ T ![a,h]).
-#a #h #G #L #T #Ha
+theorem cnv_dec (h) (a) (G) (L) (T): ac_props a →
+ Decidable (â\9d¨G,Lâ\9d© â\8a¢ T ![h,a]).
+#h #a #G #L #T #Ha
@(fqup_wf_ind_eq (Ⓣ) … G L T) -G -L -T #G0 #L0 #T0 #IH #G #L * * [|||| * ]
[ #s #HG #HL #HT destruct -Ha -IH
/2 width=1 by cnv_sort, or_introl/
/3 width=6 by cnv_inv_gref, or_intror/
| #p #I #V #T #HG #HL #HT destruct -Ha
elim (IH G L V) [| -IH | // ] #HV
- [ elim (IH G (L.ⓑ{I}V) T) -IH [3: // ] #HT
+ [ elim (IH G (L.ⓑ[I]V) T) -IH [3: // ] #HT
[ /3 width=1 by cnv_bind, or_introl/ ]
]
@or_intror #H
elim (IH G L V) [| -IH #HV | // ]
[ elim (IH G L T) -IH [| #HT #HV | // ]
[ #HT #HV
- elim (cnv_R_cpmhe_total … HT) #n #Hn
- elim (dec_min (R_cpmhe h G L T) … Hn) -Hn
- [| /2 width=2 by cnv_R_cpmhe_dec/ ] #n0 #_ -n
+ elim (cnv_R_cpmuwe_total … HT) #n #Hn
+ elim (dec_min (R_cpmuwe h G L T) … Hn) -Hn
+ [| /2 width=2 by cnv_R_cpmuwe_dec/ ] #n0 #_ -n
elim (ac_dec … Ha n0) -Ha
- [ * #n #Hn #Ha * #X0 #HX0 #_
+ [ * #n #Ha #Hn * #X0 #HX0 #_
elim (abst_dec X0)
[ * #p #W #U0 #H destruct
elim (cnv_cpes_dec … 1 0 … HV W) [ #HVW | #HnVW ]
- [ lapply (cpmhe_fwd_cpms … HX0) -HX0 #HTU0
+ [ lapply (cpmuwe_fwd_cpms … HX0) -HX0 #HTU0
elim (cnv_fwd_cpms_abst_dx_le … HT … HTU0 … Hn) #U #HTU #_ -U0 -n0
/3 width=7 by cnv_appl_cpes, or_introl/
(* Note: argument type mismatch *)
| @or_intror #H -n
elim (cnv_inv_appl_cpes … H) -H #m0 #q #WX #UX #_ #_ #_ #HVWX #HTUX
- lapply (cpmhe_abst … HTUX) -HTUX #HTUX
- elim (cnv_cpmhe_mono … HT … HTUX … HX0) -a -T #H #_
+ lapply (cpmuwe_abst … HTUX) -HTUX #HTUX
+ elim (cnv_cpmuwe_mono … HT … HTUX … HX0) -a -T #H #_
elim (cpes_fwd_abst_bi … H) -H #_ #HWX -n0 -m0 -p -q -UX -U0
/3 width=3 by cpes_cpes_trans/
- | lapply (cnv_cpmhe_trans … HT … HX0) -T #H
+ | lapply (cnv_cpmuwe_trans … HT … HX0) -T #H
elim (cnv_inv_bind … H) -H #HW #_ //
]
(* Note: no expected type *)
| #HnX0
@or_intror #H
elim (cnv_inv_appl_cpes … H) -H #m0 #q #W0 #U0 #_ #_ #_ #_ #HTU0
- lapply (cpmhe_abst … HTU0) -HTU0 #HTU0
- elim (cnv_cpmhe_mono … HT … HTU0 … HX0) -T #_ #H
- elim (theq_inv_pair1 … H) -W0 -U0 #W0 #U0 #H destruct
+ lapply (cpmuwe_abst … HTU0) -HTU0 #HTU0
+ elim (cnv_cpmuwe_mono … HT … HTU0 … HX0) -T #_ #H
+ elim (teqw_inv_abst_sn … H) -W0 -U0 #W0 #U0 #H destruct
/2 width=4 by/
]
(* Note: failed applicability *)
@or_intror #H
elim (cnv_inv_appl … H) -H #m0 #q #W0 #U0 #Hm0 #_ #_ #_ #HTU0
elim (lt_or_ge m0 n0) #H0 [| /3 width=3 by ex2_intro/ ] -Hm0 -Hge
- /4 width=6 by cpmhe_abst, ex_intro/
+ /4 width=6 by cpmuwe_abst, ex_intro/
]
]
]