#I #L #V >append_length //
qed.
-(* Basic_1: was just: chead_ctail *)
lemma lpair_ltail: ∀L,I,V. ∃∃J,K,W. L.ⓑ{I}V = ⓑ{J}W.K & |L| = |K|.
#L elim L -L /2 width=5 by ex2_3_intro/
#L #Z #X #IHL #I #V elim (IHL Z X) -IHL
(* Basic eliminators ********************************************************)
-(* Basic_1: was: c_tail_ind *)
lemma lenv_ind_alt: ∀R:predicate lenv.
R (⋆) → (∀I,L,T. R L → R (ⓑ{I}T.L)) →
∀L. R L.