Record retract (A B:Prop) : Prop :=
{f1 : A -> B; f2 : B -> A; f1_o_f2 : forall x:B, f1 (f2 x) = x}.

Lemma prop_ext_retract_A_A_imp_A :
prop_extensionality -> forall A:Prop, inhabited A -> retract A (A -> A).