apply bind_congr
α : Type u
m : Type v → Type w
inst✝¹ : Monad m
β : Type v
inst✝ : LawfulMonad m
f : α → m β
x✝ : Array α
a✝ a : α
x : Array α
IH :
  mapM f (push x a✝) = do
    let y ← mapM f x
    let b ← f a✝
    pure (push y b)
⊢ (do
      let b ← f a
      let y ← mapM f (push x a✝)
      pure (cons b y)) =
    do
    let x_1 ← f a
    let x ← mapM f x
    let y ← pure (cons x_1 x)
    let b ← f a✝
    pure (push y b)
case h
α : Type u
m : Type v → Type w
inst✝¹ : Monad m
β : Type v
inst✝ : LawfulMonad m
f : α → m β
x✝ : Array α
a✝ a : α
x : Array α
IH :
  mapM f (push x a✝) = do
    let y ← mapM f x
    let b ← f a✝
    pure (push y b)
⊢ ∀ (a : β),
    (do
        let y ← mapM f (push x a✝)
        pure (cons a y)) =
      do
      let x ← mapM f x
      let y ← pure (cons a x)
      let b ← f a✝
      pure (push y b)