(* Inversion lemmas on pointwise union for local environments ****************)
lemma llpx_sn_llor_fwd_sn: ∀R. (∀L. reflexive … (R L)) →
- ∀L1,L2,T,d. llpx_sn R d T L1 L2 →
- â\88\80L. L1 â©\96[T, d] L2 ≡ L → lpx_sn R L1 L.
-#R #HR #L1 #L2 #T #d #H1 #L #H2
+ ∀L1,L2,T,l. llpx_sn R l T L1 L2 →
+ â\88\80L. L1 â\8b\93[T, l] L2 ≡ L → lpx_sn R L1 L.
+#R #HR #L1 #L2 #T #l #H1 #L #H2
elim (llpx_sn_llpx_sn_alt … H1) -H1 #HL12 #IH1
elim H2 -H2 #_ #HL1 #IH2
@lpx_sn_intro_alt // #I1 #I #K1 #K #V1 #V #i #HLK1 #HLK