(* Properties on lazy equivalence for local environments ********************)
-lemma lleq_cpxs_trans: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 →
- â\88\80L1. L1 â\89¡[T1, 0] L2 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2.
+lemma lleq_cpxs_trans: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â¬\88*[h, o] T2 →
+ â\88\80L1. L1 â\89¡[T1, 0] L2 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] T2.
#h #o #G #L2 #T1 #T2 #H @(cpxs_ind_dx … H) -T1
/4 width=6 by cpx_lleq_conf_dx, lleq_cpx_trans, cpxs_strap2/
qed-.
-lemma cpxs_lleq_conf: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 →
- â\88\80L1. L2 â\89¡[T1, 0] L1 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2.
+lemma cpxs_lleq_conf: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â¬\88*[h, o] T2 →
+ â\88\80L1. L2 â\89¡[T1, 0] L1 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] T2.
/3 width=3 by lleq_cpxs_trans, lleq_sym/ qed-.
-lemma cpxs_lleq_conf_dx: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 →
+lemma cpxs_lleq_conf_dx: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â¬\88*[h, o] T2 →
∀L1. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
#h #o #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_lleq_conf_dx/
qed-.
-lemma cpxs_lleq_conf_sn: â\88\80h,o,G,L1,T1,T2. â¦\83G, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2 →
+lemma cpxs_lleq_conf_sn: â\88\80h,o,G,L1,T1,T2. â¦\83G, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] T2 →
∀L2. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
/4 width=6 by cpxs_lleq_conf_dx, lleq_sym/ qed-.