(* *)
(**************************************************************************)
-include "basic_2/reduction/llpr_ldrop.ma".
+include "basic_2/reduction/cpr_lift.ma".
include "basic_2/computation/cprs.ma".
(* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
(* Note: apparently this was missing in basic_1 *)
lemma cprs_delta: ∀G,L,K,V,V2,i.
- â\87©[i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V ➡* V2 →
- â\88\80W2. â\87§[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡* W2.
+ â¬\87[i] L ≡ K.ⓓV → ⦃G, K⦄ ⊢ V ➡* V2 →
+ â\88\80W2. â¬\86[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡* W2.
#G #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=6 by cpr_cprs, cpr_delta/ ]
#V1 #V2 #_ #HV12 #IHV1 #W2 #HVW2
-lapply (ldrop_fwd_drop2 … HLK) -HLK #HLK
+lapply (drop_fwd_drop2 … HLK) -HLK #HLK
elim (lift_total V1 0 (i+1)) /4 width=12 by cpr_lift, cprs_strap1/
qed.
-lemma cprs_llpr_conf: ∀G. s_r_confluent1 … (cprs G) (llpr G 0).
-/3 width=5 by llpr_cpr_conf, s_r_conf1_LTC1/ qed-.
-
(* Advanced inversion lemmas ************************************************)
(* Basic_1: was: pr3_gen_lref *)
lemma cprs_inv_lref1: ∀G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡* T2 →
T2 = #i ∨
- â\88\83â\88\83K,V1,T1. â\87©[i] L ≡ K.ⓓV1 & ⦃G, K⦄ ⊢ V1 ➡* T1 &
- â\87§[0, i + 1] T1 ≡ T2.
+ â\88\83â\88\83K,V1,T1. â¬\87[i] L ≡ K.ⓓV1 & ⦃G, K⦄ ⊢ V1 ➡* T1 &
+ â¬\86[0, i + 1] T1 ≡ T2.
#G #L #T2 #i #H @(cprs_ind … H) -T2 /2 width=1 by or_introl/
#T #T2 #_ #HT2 *
[ #H destruct
elim (cpr_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/
* /4 width=6 by cpr_cprs, ex3_3_intro, or_intror/
| * #K #V1 #T1 #HLK #HVT1 #HT1
- lapply (ldrop_fwd_drop2 … HLK) #H0LK
+ lapply (drop_fwd_drop2 … HLK) #H0LK
elim (cpr_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T
- /4 width=6 by cprs_strap1, ex3_3_intro, or_intror/
+ /4 width=6 by cprs_strap1, ex3_3_intro, or_intror/
]
qed-.