simpa using ih
case succ
n i : Nat
hi : Nat.succ i ≤ n
acc : List (Fin n)
ih :
  fins.finsAux (Nat.succ n) i ⋯ (map Fin.castSucc ({ val := i, isLt := hi } :: acc) ++ [Fin.last n]) =
    map Fin.castSucc (fins.finsAux n i ⋯ ({ val := i, isLt := hi } :: acc)) ++ [Fin.last n]
⊢ fins.finsAux (Nat.succ n) i ⋯ ({ val := i, isLt := ⋯ } :: (map Fin.castSucc acc ++ [Fin.last n])) =
    map Fin.castSucc (fins.finsAux n i ⋯ ({ val := i, isLt := hi } :: acc)) ++ [Fin.last n]
no goals