induction cs with
| nil => rfl
| cons c cs ih =>
  rw [ih]
  simp only [Schema.flattenList]
  apply Schema.retypeColumn_preserves_names
  exact Table.mk []
η : Type u_η
dec_η : DecidableEq η
sch : Schema
t : Table sch
cs : ActionList Schema.flattenList sch
⊢ List.map Prod.fst (Schema.flattenLists sch cs) = List.map Prod.fst sch
no goals