(***********************************************************************)


Inductive le_app_spec (ni1 : nested_imps) (n : nat) : Set :=
    Le_App_Spec_Intro :
      forall ni11 ni12 : nested_imps,
      ni1 = ni11 ++ ni12 -> length ni11 = n -> le_app_spec ni1 n.(***********************************************************************)


Inductive le_app_spec (ni1 : nested_imps) (n : nat) : Set :=
    Le_App_Spec_Intro :
      forall ni11 ni12 : nested_imps,
      ni1 = ni11 ++ ni12 -> length ni11 = n -> le_app_spec ni1 n.

Lemma le_app0 : forall ni1 ni21 ni22 : nested_imps, le_ni ni1 (ni21 ++ ni22) -> le_app_spec ni1 (length ni21).