(* *)
(**************************************************************************)
-include "basic_2/rt_computation/cpue_csx.ma".
-include "basic_2/rt_equivalence/cpes_cprs.ma".
-include "basic_2/dynamic/cnv_cpue.ma".
+include "basic_2/rt_computation/cpmuwe_cpmuwe.ma".
+include "basic_2/rt_equivalence/cpes_cpes.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):
- Decidable (â¦\83G,Lâ¦\84 â\8a¢ T ![a,h]).
-#a #h #G #L #T
+theorem cnv_dec (h) (a) (G) (L) (T): ac_props a →
+ Decidable (â\9dªG,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 -IH
+[ #s #HG #HL #HT destruct -Ha -IH
/2 width=1 by cnv_sort, or_introl/
-| #i #HG #HL #HT destruct
+| #i #HG #HL #HT destruct -Ha
elim (drops_F_uni L i) [| * * ]
[ /3 width=8 by cnv_inv_lref_atom, or_intror/
| /3 width=9 by cnv_inv_lref_unit, or_intror/
| /4 width=5 by cnv_inv_lref_pair, or_intror/
]
]
-| #l #HG #HL #HT destruct -IH
+| #l #HG #HL #HT destruct -Ha -IH
/3 width=6 by cnv_inv_gref, or_intror/
-| #p #I #V #T #HG #HL #HT destruct
+| #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
| #V #T #HG #HL #HT destruct
elim (IH G L V) [| -IH #HV | // ]
[ elim (IH G L T) -IH [| #HT #HV | // ]
- [ cases a -a [ * [| #a ]] #HT #HV
- [ @or_intror #H
- elim (cnv_inv_appl … H) -H #n #p #W #U #H #_ #_ #_ #_
- /3 width=2 by lt_zero_false, ylt_inv_inj/
- | elim (cnv_fwd_aaa … HT) #A #HA
- elim (cpme_total_aaa h a … HA) #X
- elim (abst_dec X) [ * ]
- [ #p #W #U #H #HTU destruct
+ [ #HT #HV
+ 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 #Ha #Hn * #X0 #HX0 #_
+ elim (abst_dec X0)
+ [ * #p #W #U0 #H destruct
elim (cnv_cpes_dec … 1 0 … HV W) [ #HVW | #HnVW ]
- [ elim HTU -HTU #HTU #_
- /4 width=7 by ylt_inj, cnv_appl_cpes, or_introl/
- | @or_intror #H
- elim (cnv_inv_appl_pred_cpes … H) -H #q #W0 #U0 #_ #_ #HVW0 #HTU0
- elim (cnv_cpme_cpms_conf … HT … HTU0 … HTU) -T #HU0 #_
- elim (cpms_inv_abst_bi … HU0) -HU0 #_ #HW0 #_ -p -q -U0
- /3 width=3 by cpes_cprs_trans/
- | lapply (cnv_cpme_trans … HT … HTU) -T #H
+ [ 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 (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_cpmuwe_trans … HT … HX0) -T #H
elim (cnv_inv_bind … H) -H #HW #_ //
]
- | #HnTU #HTX
+(* Note: no expected type *)
+ | #HnX0
@or_intror #H
- elim (cnv_inv_appl_pred_cpes … H) -H #q #W0 #U0 #_ #_ #_ #HTU0
- elim (cnv_cpme_cpms_conf … HT … HTU0 … HTX) -T #HX #_
- elim (cpms_inv_abst_sn … HX) -HX #V0 #T0 #_ #_ #H destruct -W0 -U0
- /2 width=4 by/
- ]
- | elim (cpue_total_csx h G L T)
- [| /3 width=2 by cnv_fwd_fsb, fsb_inv_csx/ ] #X
- elim (abst_dec X) [ * ]
- [ #p #W #U #H #HTU destruct
- elim (cnv_cpes_dec … 1 0 … HV W) [ #HVW | #HnVW ]
- [ elim HTU -HTU #n #HTU #_
- /3 width=7 by cnv_appl_cpes, or_introl/
- | @or_intror #H
- elim (cnv_inv_appl_cpes … H) -H #m1 #q #W0 #U0 #_ #_ #_ #HVW0 #HTU0
- elim (cnv_cpue_cpms_conf … HT … HTU0 … HTU) -m1 -T #X * #m2 #HU0X #_ #HUX
- elim (tueq_inv_bind1 … HUX) -HUX #X0 #_ #H destruct -U
- elim (cpms_inv_abst_bi … HU0X) -HU0X #_ #HW0 #_ -p -q -m2 -U0 -X0
- /3 width=3 by cpes_cprs_trans/
- | lapply (cnv_cpue_trans … HT … HTU) -T #H
- elim (cnv_inv_bind … H) -H #HW #_ //
- ]
- | #HnTU #HTX
- @or_intror #H
- elim (cnv_inv_appl_cpes … H) -H #m1 #q #W0 #U0 #_ #_ #_ #_ #HTU0
- elim (cnv_cpue_cpms_conf … HT … HTU0 … HTX) -m1 -T #X0 * #m2 #HUX0 #_ #HX0
- elim (cpms_inv_abst_sn … HUX0) -HUX0 #V0 #T0 #_ #_ #H destruct -m2 -W0 -U0
- elim (tueq_inv_bind2 … HX0) -HX0 #X0 #_ #H destruct
+ elim (cnv_inv_appl_cpes … H) -H #m0 #q #W0 #U0 #_ #_ #_ #_ #HTU0
+ lapply (cpmuwe_abst … HTU0) -HTU0 #HTU0
+ elim (cnv_cpmuwe_mono … HT … HTU0 … HX0) -T #_ #H
+ elim (tweq_inv_abst_sn … H) -W0 -U0 #W0 #U0 #H destruct
/2 width=4 by/
]
+(* Note: failed applicability *)
+ | #Hge #_ #Hlt
+ @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 cpmuwe_abst, ex_intro/
]
]
]
projects / helm.git / blobdiff