Definition var_env'_to_env'' (L U : nat) (ve : var_env') :=
match var_env'_to_var_env''_lemma2 (U - L) L U ve (refl_equal _) with
| exist ve'' _ => ve''
end.

Lemma var_env'_to_env''_lemma3 :
forall (L U : nat) (ve : var_env'),
In _ (Evar_env'' L U) (var_env'_to_env'' L U ve) /\
(forall x : ad,
var_lu L U x = true ->
in_dom _ x (var_env'_to_env'' L U ve) = ve (nat_of_N x)).