include "basic_2/reduction/lpx_lleq.ma".
include "basic_2/computation/cpxs_leq.ma".
-include "basic_2/computation/lpxs_ldrop.ma".
+include "basic_2/computation/lpxs_drop.ma".
include "basic_2/computation/lpxs_cpxs.ma".
(* SN EXTENDED PARALLEL COMPUTATION FOR LOCAL ENVIRONMENTS ******************)
[ #I #G1 #L1 #V1 #X #H1 #H2 elim (lpxs_inv_pair2 … H1) -H1
#K0 #V0 #H1KL1 #_ #H destruct
elim (lleq_inv_lref_ge_dx … H2 ? I L1 V1) -H2 //
- #K1 #H #H2KL1 lapply (ldrop_inv_O2 … H) -H #H destruct
+ #K1 #H #H2KL1 lapply (drop_inv_O2 … H) -H #H destruct
/2 width=4 by fqu_lref_O, ex3_intro/
| * [ #a ] #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H
[ elim (lleq_inv_bind … H)
| #I #G1 #L1 #V1 #T1 #K1 #HLK1 #H elim (lleq_inv_flat … H) -H
/2 width=4 by fqu_flat_dx, ex3_intro/
| #G1 #L1 #L #T1 #U1 #e #HL1 #HTU1 #K1 #H1KL1 #H2KL1
- elim (ldrop_O1_le (Ⓕ) (e+1) K1)
+ elim (drop_O1_le (Ⓕ) (e+1) K1)
[ #K #HK1 lapply (lleq_inv_lift_le … H2KL1 … HK1 HL1 … HTU1 ?) -H2KL1 //
- #H2KL elim (lpxs_ldrop_trans_O1 … H1KL1 … HL1) -L1
- #K0 #HK10 #H1KL lapply (ldrop_mono … HK10 … HK1) -HK10 #H destruct
+ #H2KL elim (lpxs_drop_trans_O1 … H1KL1 … HL1) -L1
+ #K0 #HK10 #H1KL lapply (drop_mono … HK10 … HK1) -HK10 #H destruct
/3 width=4 by fqu_drop, ex3_intro/
- | lapply (ldrop_fwd_length_le2 … HL1) -L -T1 -g
+ | lapply (drop_fwd_length_le2 … HL1) -L -T1 -g
lapply (lleq_fwd_length … H2KL1) //
]
]
]
qed-.
-fact leq_lpxs_trans_lleq_aux: â\88\80h,g,G,L1,L0,d,e. L1 â\89\83[d, e] L0 → e = ∞ →
+fact leq_lpxs_trans_lleq_aux: â\88\80h,g,G,L1,L0,d,e. L1 ⩬[d, e] L0 → e = ∞ →
∀L2. ⦃G, L0⦄ ⊢ ➡*[h, g] L2 →
- â\88\83â\88\83L. L â\89\83[d, e] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L &
+ â\88\83â\88\83L. L ⩬[d, e] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L &
(∀T. L0 ≡[T, d] L2 ↔ L1 ≡[T, d] L).
#h #g #G #L1 #L0 #d #e #H elim H -L1 -L0 -d -e
[ #d #e #_ #L2 #H >(lpxs_inv_atom1 … H) -H
]
qed-.
-lemma leq_lpxs_trans_lleq: â\88\80h,g,G,L1,L0,d. L1 â\89\83[d, ∞] L0 →
+lemma leq_lpxs_trans_lleq: â\88\80h,g,G,L1,L0,d. L1 ⩬[d, ∞] L0 →
∀L2. ⦃G, L0⦄ ⊢ ➡*[h, g] L2 →
- â\88\83â\88\83L. L â\89\83[d, ∞] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L &
+ â\88\83â\88\83L. L ⩬[d, ∞] L2 & ⦃G, L1⦄ ⊢ ➡*[h, g] L &
(∀T. L0 ≡[T, d] L2 ↔ L1 ≡[T, d] L).
/2 width=1 by leq_lpxs_trans_lleq_aux/ qed-.