Inductive sig2 (A : Type) (P Q : A -> Prop) : Type :=
    exist2 : forall x : A, P x -> Q x -> {x : A | P x & Q x}

Arguments sig2 [A%type_scope] _%type_scope _%type_scope
Arguments exist2 [A%type_scope] _%function_scope _%function_scope
exists x : nat, x = x
     : Prop
fun b : bool => if b then b else b
     : bool -> bool