∀ {α : Type u_9} {M : Type u_10} {inst : Zero M} {support : Finset α} {toFun : α → M}
  {mem_support_toFun : ∀ (a : α), a ∈ support ↔ toFun a ≠ 0} {support_1 : Finset α} {toFun_1 : α → M}
  {mem_support_toFun_1 : ∀ (a : α), a ∈ support_1 ↔ toFun_1 a ≠ 0},
  { support := support, toFun := toFun, mem_support_toFun := mem_support_toFun } =
      { support := support_1, toFun := toFun_1, mem_support_toFun := mem_support_toFun_1 } →
    support = support_1 ∧ toFun = toFun_1