include "basic_2/notation/relations/ineint_5.ma".
include "basic_2/grammar/aarity.ma".
-include "basic_2/substitution/gr2_gr2.ma".
-include "basic_2/substitution/lifts_lift_vector.ma".
-include "basic_2/substitution/ldrops_ldrop.ma".
+include "basic_2/multiple/gr2_gr2.ma".
+include "basic_2/multiple/lifts_lift_vector.ma".
+include "basic_2/multiple/drops_drop.ma".
include "basic_2/computation/acp.ma".
(* ABSTRACT COMPUTATION PROPERTIES ******************************************)
∀A. acr RR RS RP (aacr RP A).
#RR #RS #RP #H1RP #H2RP #A elim A -A normalize //
#B #A #IHB #IHA @mk_acr normalize
-[ /3 width=7 by ldrops_cons, lifts_cons/
+[ /3 width=7 by drops_cons, lifts_cons/
| #G #L #T #H
elim (cp1 … H1RP G L) #k #HK
lapply (H ? (⋆k) ? (⟠) ? ? ?) -H
| #H @(cp2 … H1RP … k) @(s1 … IHA) //
]
| #G #L #Vs #HVs #T #H1T #H2T #L0 #V0 #X #des #HB #HL0 #H
- elim (lifts_inv_applv1 … H) -H #V0s #T0 #HV0s #HT0 #H destruct
+ elim (lifts_inv_appls1 … H) -H #V0s #T0 #HV0s #HT0 #H destruct
lapply (s1 … IHB … HB) #HV0
@(s2 … IHA … (V0 @ V0s))
/3 width=14 by rp_liftsv_all, acp_lifts, cp0, lifts_simple_dx, conj/
| #a #G #L #Vs #U #T #W #HA #L0 #V0 #X #des #HB #HL0 #H
- elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
+ elim (lifts_inv_appls1 … H) -H #V0s #Y #HV0s #HY #H destruct
elim (lifts_inv_flat1 … HY) -HY #U0 #X #HU0 #HX #H destruct
elim (lifts_inv_bind1 … HX) -HX #W0 #T0 #HW0 #HT0 #H destruct
- @(s3 … IHA … (V0 @ V0s)) /5 width=6 by lifts_applv, lifts_flat, lifts_bind/
+ @(s3 … IHA … (V0 @ V0s)) /5 width=6 by lifts_appls, lifts_flat, lifts_bind/
| #G #L #Vs #HVs #k #L0 #V0 #X #des #HB #HL0 #H
- elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
+ elim (lifts_inv_appls1 … H) -H #V0s #Y #HV0s #HY #H destruct
>(lifts_inv_sort1 … HY) -Y
lapply (s1 … IHB … HB) #HV0
@(s4 … IHA … (V0 @ V0s)) /3 width=7 by rp_liftsv_all, conj/
| #I #G #L #K #Vs #V1 #V2 #i #HA #HV12 #HLK #L0 #V0 #X #des #HB #HL0 #H
- elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
+ elim (lifts_inv_appls1 … H) -H #V0s #Y #HV0s #HY #H destruct
elim (lifts_inv_lref1 … HY) -HY #i0 #Hi0 #H destruct
- elim (ldrops_ldrop_trans … HL0 … HLK) #X #des0 #i1 #HL02 #H #Hi1 #Hdes0
+ elim (drops_drop_trans … HL0 … HLK) #X #des0 #i1 #HL02 #H #Hi1 #Hdes0
>(at_mono … Hi1 … Hi0) in HL02; -i1 #HL02
- elim (ldrops_inv_skip2 … Hdes0 … H) -H -des0 #L2 #W1 #des0 #Hdes0 #HLK #HVW1 #H destruct
+ elim (drops_inv_skip2 … Hdes0 … H) -H -des0 #L2 #W1 #des0 #Hdes0 #HLK #HVW1 #H destruct
elim (lift_total W1 0 (i0 + 1)) #W2 #HW12
elim (lifts_lift_trans … Hdes0 … HVW1 … HW12) // -Hdes0 -Hi0 #V3 #HV13 #HVW2
>(lift_mono … HV13 … HV12) in HVW2; -V3 #HVW2
- @(s5 … IHA … (V0 @ V0s) … HW12 HL02) /3 width=5 by lifts_applv/
+ @(s5 … IHA … (V0 @ V0s) … HW12 HL02) /3 width=5 by lifts_appls/
| #G #L #V1s #V2s #HV12s #a #V #T #HA #HV #L0 #V10 #X #des #HB #HL0 #H
- elim (lifts_inv_applv1 … H) -H #V10s #Y #HV10s #HY #H destruct
+ elim (lifts_inv_appls1 … H) -H #V10s #Y #HV10s #HY #H destruct
elim (lifts_inv_bind1 … HY) -HY #V0 #T0 #HV0 #HT0 #H destruct
elim (lift_total V10 0 1) #V20 #HV120
elim (liftv_total 0 1 V10s) #V20s #HV120s
@(s6 … IHA … (V10 @ V10s) (V20 @ V20s)) /3 width=7 by rp_lifts, liftv_cons/
- @(HA … (des + 1)) /2 width=2 by ldrops_skip/
- [ @(s0 … IHB … HB … HV120) /2 width=2 by ldrop_drop/
- | @lifts_applv //
+ @(HA … (des + 1)) /2 width=2 by drops_skip/
+ [ @(s0 … IHB … HB … HV120) /2 width=2 by drop_drop/
+ | @lifts_appls //
elim (liftsv_liftv_trans_le … HV10s … HV120s) -V10s #V10s #HV10s #HV120s
>(liftv_mono … HV12s … HV10s) -V1s //
]
| #G #L #Vs #T #W #HA #HW #L0 #V0 #X #des #HB #HL0 #H
- elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
+ elim (lifts_inv_appls1 … H) -H #V0s #Y #HV0s #HY #H destruct
elim (lifts_inv_flat1 … HY) -HY #W0 #T0 #HW0 #HT0 #H destruct
- @(s7 … IHA … (V0 @ V0s)) /3 width=5 by lifts_applv/
+ @(s7 … IHA … (V0 @ V0s)) /3 width=5 by lifts_appls/
]
qed.