induction' as with a as ih generalizing bs
α✝ : Type u
inst✝² : DecidableEq α✝
β✝ : Type v
inst✝¹ : DecidableEq β✝
m : Type ?u.157952 → Type ?u.157954
α : Type u_2
β : Type u_1
inst✝ : Monad m
bs : List β
b : β
f : α → Option β
as : List α
h : mapM' f as = some bs
hb : b ∈ bs
⊢ ∃ a, f a = some b
case nil
α✝ : Type u
inst✝² : DecidableEq α✝
β✝ : Type v
inst✝¹ : DecidableEq β✝
m : Type ?u.157952 → Type ?u.157954
α : Type u_2
β : Type u_1
inst✝ : Monad m
b : β
f : α → Option β
bs : List β
h : mapM' f [] = some bs
hb : b ∈ bs
⊢ ∃ a, f a = some b

case cons
α✝ : Type u
inst✝² : DecidableEq α✝
β✝ : Type v
inst✝¹ : DecidableEq β✝
m : Type ?u.157952 → Type ?u.157954
α : Type u_2
β : Type u_1
inst✝ : Monad m
b : β
f : α → Option β
a : α
as : List α
ih : ∀ {bs : List β}, mapM' f as = some bs → b ∈ bs → ∃ a, f a = some b
bs : List β
h : mapM' f (a :: as) = some bs
hb : b ∈ bs
⊢ ∃ a, f a = some b