(* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
-(* Properties on poinwise union for local environments **********************)
+(* Properties on pointwise union for local environments **********************)
lemma llpx_sn_llor_dx: ∀R. (s_r_confluent1 … R (llpx_sn R 0)) → (frees_trans R) →
- â\88\80L1,L2,T,d. llpx_sn R d T L1 L2 â\86\92 â\88\80L. L1 â©\96[T, d] L2 ≡ L → L2 ≡[T, d] L.
+ â\88\80L1,L2,T,d. llpx_sn R d T L1 L2 â\86\92 â\88\80L. L1 â\8b\93[T, d] L2 ≡ L → L2 ≡[T, d] L.
#R #H1R #H2R #L1 #L2 #T #d #H1 #L #H2
lapply (llpx_sn_frees_trans … H1R H2R … H1) -H1R -H2R #HR
elim (llpx_sn_llpx_sn_alt … H1) -H1 #HL12 #IH1
qed.
lemma llpx_sn_llor_dx_sym: ∀R. (s_r_confluent1 … R (llpx_sn R 0)) → (frees_trans R) →
- â\88\80L1,L2,T,d. llpx_sn R d T L1 L2 â\86\92 â\88\80L. L1 â©\96[T, d] L2 ≡ L → L ≡[T, d] L2.
+ â\88\80L1,L2,T,d. llpx_sn R d T L1 L2 â\86\92 â\88\80L. L1 â\8b\93[T, d] L2 ≡ L → L ≡[T, d] L2.
/3 width=6 by llpx_sn_llor_dx, lleq_sym/ qed.