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 all_mono_lm_to_ml_mono {A:Type} (lm: list (monad A)): Forall Mmono lm → Mmono (lm_to_ml lm).