Require Import ssreflect ssrbool.

Set Implicit Arguments.

  Inductive wf T : bool -> option T -> Type :=
  | wf_f : wf false None
  | wf_t : forall x, wf true (Some x).

  Derive Inversion wf_inv with (forall T b (o : option T), wf b o) Sort Prop.

  Lemma Problem T b (o : option T) :
    wf b o ->
    match b with
    | true  => exists x, o = Some x
    | false => o = None
    end.
  Proof.
  by case: b; elim/wf_inv=>//;case: o=>// a *; exists a.
  Qed.