(* *)
(**************************************************************************)
-include "basic_2/substitution/lifts_lifts.ma".
-include "basic_2/substitution/ldrops_ldrops.ma".
+include "basic_2/multiple/lifts_lifts.ma".
+include "basic_2/multiple/ldrops_ldrops.ma".
include "basic_2/static/aaa_lifts.ma".
include "basic_2/static/aaa_aaa.ma".
include "basic_2/computation/lsubc_ldrops.ma".
theorem aacr_aaa_csubc_lifts: ∀RR,RS,RP.
acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
∀G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A → ∀L0,des. ⇩*[Ⓕ, des] L0 ≡ L1 →
- â\88\80T0. â\87§*[des] T â\89¡ T0 â\86\92 â\88\80L2. G â\8a¢ L2 â\8a\91[RP] L0 →
+ â\88\80T0. â\87§*[des] T â\89¡ T0 â\86\92 â\88\80L2. G â\8a¢ L2 â«\83[RP] L0 →
⦃G, L2, T0⦄ ϵ[RP] 〚A〛.
#RR #RS #RP #H1RP #H2RP #G #L1 #T #A #H elim H -G -L1 -T -A
[ #G #L #k #L0 #des #HL0 #X #H #L2 #HL20
elim (lift_total V0 0 (i0 +1)) #V3 #HV03
elim (lift_total V2 0 (i0 +1)) #V #HV2
@(s5 … HB … (◊) … (ⓝV3.V) … HLK2) [2: /2 width=1 by lift_flat/ ]
- @(s7 … HB … (◊)) [ @(s8 … HB … HKV2A) // | @(s8 … HB … H1KV0A) // ]
+ @(s7 … HB … (◊)) [ @(s0 … HB … HKV2A) // | @(s0 … HB … H1KV0A) // ]
]
| #a #G #L #V #T #B #A #_ #_ #IHB #IHA #L0 #des #HL0 #X #H #L2 #HL20
elim (lifts_inv_bind1 … H) -H #V0 #T0 #HV0 #HT0 #H destruct