Definition Mbind2 {A B C:Type} (mab:monad (A*B)) (f:A→B→monad C) :=
(λ st, let (st',ab):= Meval mab st in let m':=f (fst ab) (snd ab) in m' st'):monad C.
Infix ">>==" := Mbind2 (at level 15, left associativity) : monad_scope.

Lemma lt_le_Mbind2_lt {A B C:Type} (mab:monad (A*B)) (f:A→B→monad C):
Mlt mab → (∀ a b, Mle (f a b)) → Mlt (mab >>== f).