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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.
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