(* *)
(**************************************************************************)
-include "Basic_2/static/aaa_lift.ma".
-include "Basic_2/computation/acp_cr.ma".
-include "Basic_2/computation/lsubc.ma".
+include "basic_2/static/aaa_lift.ma".
+include "basic_2/computation/acp_cr.ma".
+include "basic_2/computation/lsubc.ma".
(* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
(* Properties concerning basic local environment slicing ********************)
(* Basic_1: was: csubc_drop_conf_O *)
-(* Note: the constant (0) can not be generalized *)
-lemma lsubc_ldrop_O1_trans: ∀RP,L1,L2. L1 [RP] ⊑ L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
- ∃∃K1. ⇩[0, e] L1 ≡ K1 & K1 [RP] ⊑ K2.
+(* Note: the constant 0 can not be generalized *)
+lemma lsubc_ldrop_O1_trans: ∀RP,L1,L2. L1 ⊑[RP] L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
+ ∃∃K1. ⇩[0, e] L1 ≡ K1 & K1 ⊑[RP] K2.
#RP #L1 #L2 #H elim H -L1 -L2
[ #X #e #H
>(ldrop_inv_atom1 … H) -H /2 width=3/
(* Basic_1: was: csubc_drop_conf_rev *)
lemma ldrop_lsubc_trans: ∀RR,RS,RP.
acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
- ∀L1,K1,d,e. ⇩[d, e] L1 ≡ K1 → ∀K2. K1 [RP] ⊑ K2 →
- ∃∃L2. L1 [RP] ⊑ L2 & ⇩[d, e] L2 ≡ K2.
+ ∀L1,K1,d,e. ⇩[d, e] L1 ≡ K1 → ∀K2. K1 ⊑[RP] K2 →
+ ∃∃L2. L1 ⊑[RP] L2 & ⇩[d, e] L2 ≡ K2.
#RR #RS #RP #Hacp #Hacr #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
[ #d #e #X #H
>(lsubc_inv_atom1 … H) -H /2 width=3/