(* *)
(**************************************************************************)
-include "basic_2/rt_computation/lpxs_rdeq.ma".
+include "basic_2/rt_computation/lpxs_reqx.ma".
include "basic_2/rt_computation/lpxs_lpxs.ma".
include "basic_2/rt_computation/rsx_rsx.ma".
(* Eliminators with unbound rt-computation for full local environments ******)
-lemma rsx_ind_lpxs_rdeq (h) (G) (T) (Q:predicate lenv):
+lemma rsx_ind_lpxs_reqx (h) (G) (T) (Q:predicate lenv):
(āL1. G ā¢ ā¬*[h,T] šā¦L1ā¦ ā
(āL2. ā¦G,L1ā¦ ā¢ ā¬*[h] L2 ā (L1 ā[T] L2 ā ā„) ā Q L2) ā
Q L1
āL0. ā¦G,L1ā¦ ā¢ ā¬*[h] L0 ā āL2. L0 ā[T] L2 ā Q L2.
#h #G #T #Q #IH #L1 #H @(rsx_ind ā¦ H) -L1
#L1 #HL1 #IH1 #L0 #HL10 #L2 #HL02
-@IH -IH /3 width=3 by rsx_lpxs_trans, rsx_rdeq_trans/ -HL1 #K2 #HLK2 #HnLK2
-lapply (rdeq_rdneq_trans ā¦ HL02 ā¦ HnLK2) -HnLK2 #H
-elim (rdeq_lpxs_trans ā¦ HLK2 ā¦ HL02) -L2 #K0 #HLK0 #HK02
-lapply (rdneq_rdeq_canc_dx ā¦ H ā¦ HK02) -H #HnLK0
-elim (rdeq_dec L1 L0 T) #H
-[ lapply (rdeq_rdneq_trans ā¦ H ā¦ HnLK0) -H -HnLK0 #Hn10
+@IH -IH /3 width=3 by rsx_lpxs_trans, rsx_reqx_trans/ -HL1 #K2 #HLK2 #HnLK2
+lapply (reqx_rneqx_trans ā¦ HL02 ā¦ HnLK2) -HnLK2 #H
+elim (reqx_lpxs_trans ā¦ HLK2 ā¦ HL02) -L2 #K0 #HLK0 #HK02
+lapply (rneqx_reqx_canc_dx ā¦ H ā¦ HK02) -H #HnLK0
+elim (reqx_dec L1 L0 T) #H
+[ lapply (reqx_rneqx_trans ā¦ H ā¦ HnLK0) -H -HnLK0 #Hn10
lapply (lpxs_trans ā¦ HL10 ā¦ HLK0) -L0 #H10
- elim (lpxs_rdneq_inv_step_sn ā¦ H10 ā¦ Hn10) -H10 -Hn10
- /3 width=8 by rdeq_trans/
-| elim (lpxs_rdneq_inv_step_sn ā¦ HL10 ā¦ H) -HL10 -H #L #K #HL1 #HnL1 #HLK #HKL0
- elim (rdeq_lpxs_trans ā¦ HLK0 ā¦ HKL0) -L0
- /3 width=8 by lpxs_trans, rdeq_trans/
+ elim (lpxs_rneqx_inv_step_sn ā¦ H10 ā¦ Hn10) -H10 -Hn10
+ /3 width=8 by reqx_trans/
+| elim (lpxs_rneqx_inv_step_sn ā¦ HL10 ā¦ H) -HL10 -H #L #K #HL1 #HnL1 #HLK #HKL0
+ elim (reqx_lpxs_trans ā¦ HLK0 ā¦ HKL0) -L0
+ /3 width=8 by lpxs_trans, reqx_trans/
]
qed-.
) ā
āL. G ā¢ ā¬*[h,T] šā¦Lā¦ ā Q L.
#h #G #T #Q #IH #L #HL
-@(rsx_ind_lpxs_rdeq ā¦ IH ā¦ HL) -IH -HL // (**) (* full auto fails *)
+@(rsx_ind_lpxs_reqx ā¦ IH ā¦ HL) -IH -HL // (**) (* full auto fails *)
qed-.
(* Advanced properties ******************************************************)
#Y #HY #IHY #L2 #H #HL12 destruct
@rsx_intro_lpxs #L0 #HL20
lapply (lpxs_trans ā¦ HL12 ā¦ HL20) #HL10 #H
-elim (rdneq_inv_bind ā¦ H) -H [ -IHY | -HY -IHL1 -HL12 ]
-[ #HnV elim (rdeq_dec L1 L2 V)
+elim (rneqx_inv_bind ā¦ H) -H [ -IHY | -HY -IHL1 -HL12 ]
+[ #HnV elim (reqx_dec L1 L2 V)
[ #HV @(IHL1 ā¦ HL10) -IHL1 -HL12 -HL10
- /3 width=4 by rsx_lpxs_trans, lpxs_bind_refl_dx, rdeq_canc_sn/ (**) (* full auto too slow *)
+ /3 width=4 by rsx_lpxs_trans, lpxs_bind_refl_dx, reqx_canc_sn/ (**) (* full auto too slow *)
| -HnV -HL10 /4 width=4 by rsx_lpxs_trans, lpxs_bind_refl_dx/
]
| /3 width=4 by lpxs_bind_refl_dx/
#L1 #HL1 #IHL1 #L2 #T #H @(rsx_ind_lpxs ā¦ H) -L2
#L2 #HL2 #IHL2 #HL12 @rsx_intro_lpxs
#L0 #HL20 lapply (lpxs_trans ā¦ HL12 ā¦ HL20)
-#HL10 #H elim (rdneq_inv_flat ā¦ H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
-[ #HnV elim (rdeq_dec L1 L2 V)
+#HL10 #H elim (rneqx_inv_flat ā¦ H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
+[ #HnV elim (reqx_dec L1 L2 V)
[ #HV @(IHL1 ā¦ HL10) -IHL1 -HL12 -HL10
- /3 width=5 by rsx_lpxs_trans, rdeq_canc_sn/ (**) (* full auto too slow: 47s *)
+ /3 width=5 by rsx_lpxs_trans, reqx_canc_sn/ (**) (* full auto too slow: 47s *)
| -HnV -HL10 /3 width=4 by rsx_lpxs_trans/
]
| /3 width=3 by/
#Y #HY #IHY #L2 #H #HL12 destruct
@rsx_intro_lpxs #L0 #HL20
lapply (lpxs_trans ā¦ HL12 ā¦ HL20) #HL10 #H
-elim (rdneq_inv_bind_void ā¦ H) -H [ -IHY | -HY -IHL1 -HL12 ]
-[ #HnV elim (rdeq_dec L1 L2 V)
+elim (rneqx_inv_bind_void ā¦ H) -H [ -IHY | -HY -IHL1 -HL12 ]
+[ #HnV elim (reqx_dec L1 L2 V)
[ #HV @(IHL1 ā¦ HL10) -IHL1 -HL12 -HL10
- /3 width=6 by rsx_lpxs_trans, lpxs_bind_refl_dx, rdeq_canc_sn/ (**) (* full auto too slow *)
+ /3 width=6 by rsx_lpxs_trans, lpxs_bind_refl_dx, reqx_canc_sn/ (**) (* full auto too slow *)
| -HnV -HL10 /4 width=4 by rsx_lpxs_trans, lpxs_bind_refl_dx/
]
| /3 width=4 by lpxs_bind_refl_dx/