proposition: Lemma case_L_R' {n m} (P : t (n + m) -> Type) (p : t (n + m)) : (forall q, P (L m q)) -> (forall q, P (R n q)) -> P p.
proof: Proof. induction n as [|n IH]; intros IHL IHR. - apply IHR. - apply caseS'. + apply (IHL F1). + intros p'. apply (IH (fun _ => _) p'); intros q. * apply (IHL (FS q)). * apply (IHR q). Qed.
imports: PeanoNat