(* WEIGHT OF A LOCAL ENVIRONMENT ********************************************)
rec definition lw L ≝ match L with
-[ LAtom ⇒ 0
+[ LAtom ⇒ 𝟏
| LBind L I ⇒ lw L + ♯❨I❩
].
(* Basic properties *********************************************************)
+lemma lw_atom_unfold: 𝟏 = ♯❨⋆❩.
+// qed.
+
+lemma lw_bind_unfold (I) (L): ♯❨L❩ + ♯❨I❩ = ♯❨L.ⓘ[I]❩.
+// qed.
+
(* Basic_2A1: uses: lw_pair *)
lemma lw_bind: ∀I,L. ♯❨L❩ < ♯❨L.ⓘ[I]❩.
-normalize /2 width=1 by monotonic_le_plus_r/ qed.
+// qed.
(* Basic_1: removed theorems 4: clt_cong clt_head clt_thead clt_wf_ind *)
(* Basic_1: removed local theorems 1: clt_wf__q_ind *)