fact: Definition eq_sig2_hprop_iff {A} {P Q : A -> Prop} (Q_hprop : forall (x : A) (p q : Q x), p = q) (u v : { a : A | P a & Q a }) : u = v <-> (u = v :> { a : A | P a }) := conj (fun p => f_equal (@sig_of_sig2 _ _ _) p) (eq_sig2_hprop Q_hprop u v).
imports: Notations Ltac Datatypes Logic