lemma preterm_in_root_inv_lcons_oref:
∀p,l,n. l◗p ϵ ▵#n →
- ∧∧ 𝗱❨n❩ = l & 𝐞 = p.
+ ∧∧ 𝗱n = l & 𝐞 = p.
#p #l #n * #q
<list_append_lcons_sn #H0 destruct -H0
elim (eq_inv_list_empty_append … e0) -e0 #H0 #_
lemma preterm_in_root_inv_lcons_iref:
∀t,p,l,n. l◗p ϵ ▵𝛗n.t →
- ∧∧ 𝗱❨n❩ = l & p ϵ ▵t.
+ ∧∧ 𝗱n = l & p ϵ ▵t.
#t #p #l #n * #q
<list_append_lcons_sn * #r #Hr #H0 destruct
/3 width=2 by ex_intro, conj/