Section Paradox.
Variable M : Prop -> Prop.
Hypothesis incr : forall A B:Prop, (A->B) -> M A -> M B.
(** ** The universe of modal propositions *)
Definition MProp := { P:Prop | M P -> P }.
Definition El : MProp -> Prop := @proj1_sig _ _.

Lemma modal : forall P:MProp, M(El P) -> El P.