(* Inversion lemmas with length for local environments **********************)
lemma lveq_inv_void_dx_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1, n2] L2.ⓧ → |L1| ≤ |L2| →
- â\88\83â\88\83m2. L1 â\89\8b â\93§*[n1, m2] L2 & 0 = n1 & ⫯m2 = n2.
+ â\88\83â\88\83m2. L1 â\89\8b â\93§*[n1, m2] L2 & 0 = n1 & â\86\91m2 = n2.
#L1 #L2 #n1 #n2 #H #HL12
lapply (lveq_fwd_length_plus … H) normalize >plus_n_Sm #H0
lapply (plus2_inv_le_sn … H0 HL12) -H0 -HL12 #H0
qed-.
lemma lveq_inv_void_sn_length: ∀L1,L2,n1,n2. L1.ⓧ ≋ⓧ*[n1, n2] L2 → |L2| ≤ |L1| →
- â\88\83â\88\83m1. L1 â\89\8b â\93§*[m1, n2] L2 & ⫯m1 = n1 & 0 = n2.
+ â\88\83â\88\83m1. L1 â\89\8b â\93§*[m1, n2] L2 & â\86\91m1 = n1 & 0 = n2.
#L1 #L2 #n1 #n2 #H #HL
lapply (lveq_sym … H) -H #H
elim (lveq_inv_void_dx_length … H HL) -H -HL