Inductive IfProp (A B:Prop) : bool -> Prop :=
  | Iftrue : A -> IfProp A B true
  | Iffalse : B -> IfProp A B false.Inductive IfProp (A B:Prop) : bool -> Prop :=
  | Iftrue : A -> IfProp A B true
  | Iffalse : B -> IfProp A B false.Inductive IfProp (A B:Prop) : bool -> Prop :=
  | Iftrue : A -> IfProp A B true
  | Iffalse : B -> IfProp A B false.

Lemma IfProp_true : forall A B:Prop, IfProp A B true -> A.