induction asss
α : Type u
inst✝ : Category α
asss : List (List (List α))
⊢ joinF.associatorLeft asss ≫ joinF.associatorRight asss =
    𝟙 (Prefunctor.obj (Prefunctor.obj mapF.toPrefunctor joinF ⋙ joinF).toPrefunctor asss)
case nil
α : Type u
inst✝ : Category α
⊢ joinF.associatorLeft [] ≫ joinF.associatorRight [] =
    𝟙 (Prefunctor.obj (Prefunctor.obj mapF.toPrefunctor joinF ⋙ joinF).toPrefunctor [])

case cons
α : Type u
inst✝ : Category α
head✝ : List (List α)
tail✝ : List (List (List α))
tail_ih✝ :
  joinF.associatorLeft tail✝ ≫ joinF.associatorRight tail✝ =
    𝟙 (Prefunctor.obj (Prefunctor.obj mapF.toPrefunctor joinF ⋙ joinF).toPrefunctor tail✝)
⊢ joinF.associatorLeft (head✝ :: tail✝) ≫ joinF.associatorRight (head✝ :: tail✝) =
    𝟙 (Prefunctor.obj (Prefunctor.obj mapF.toPrefunctor joinF ⋙ joinF).toPrefunctor (head✝ :: tail✝))