(* *)
(**************************************************************************)
-include "basic_2/reduction/lpx_leq.ma".
+include "basic_2/reduction/cpx_lleq.ma".
include "basic_2/computation/cpxs.ma".
(* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
(* Properties on lazy equivalence for local environments ********************)
lemma lleq_cpxs_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, g] T2 →
- â\88\80L1. L1 â\8b\95[0, T1] L2 → ⦃G, L1⦄ ⊢ T1 ➡*[h, g] T2.
+ â\88\80L1. L1 â\89¡[T1, 0] L2 → ⦃G, L1⦄ ⊢ T1 ➡*[h, g] T2.
#h #g #G #L2 #T1 #T2 #H @(cpxs_ind_dx … H) -T1
-/4 width=6 by lleq_cpx_conf_dx, lleq_cpx_trans, cpxs_strap2/
+/4 width=6 by cpx_lleq_conf_dx, lleq_cpx_trans, cpxs_strap2/
qed-.
+
+lemma cpxs_lleq_conf: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, g] T2 →
+ ∀L1. L2 ≡[T1, 0] L1 → ⦃G, L1⦄ ⊢ T1 ➡*[h, g] T2.
+/3 width=3 by lleq_cpxs_trans, lleq_sym/ qed-.
+
+lemma cpxs_lleq_conf_dx: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, g] T2 →
+ ∀L1. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
+#h #g #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_lleq_conf_dx/
+qed-.
+
+lemma cpxs_lleq_conf_sn: ∀h,g,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡*[h, g] T2 →
+ ∀L2. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
+/4 width=6 by cpxs_lleq_conf_dx, lleq_sym/ qed-.