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 Mbind2_list {A B:Type} (ma1:monad A) (mal2 mal3:monad (list A)) (mb:monad B) (f:(A*(list A)*(list A))→B→monad A) (P:A→Prop):
(∀ st, P (snd (ma1 st))) →
(∀ st, Forall P (snd (mal2 st))) →
(∀ st, Forall P (snd (mal3 st))) →
(∀ xyz, P (fst (fst xyz)) → Forall P (snd (fst xyz)) → Forall P (snd xyz) →
(∀ b st, P (snd ((f xyz b) st)))) →
∀ st, P (snd ((ma1 >>+ mal2 >>++ mal3 >>+ mb >>== f) st)).