refine ⟨fun ⟨h₀, h₁, hlt, hforall⟩ ↦ ⟨h₀, h₁, hlt, fun F hF hF₀ hF₁ ↦ ?_⟩,
  fun ⟨hF₀, hF₁, hss, hforall⟩ ↦ ⟨hF₀, hF₁, hss, ?_⟩⟩
α : Type u_1
M : Matroid α
I F X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e f : α
⊢ (∃ (h : M.Flat F₀) (h_1 : M.Flat F₁),
      ⋯.toFlatOf < ⋯.toFlatOf ∧ ∀ (c : FlatOf M), ⋯.toFlatOf ≤ c → c ≤ ⋯.toFlatOf → c = ⋯.toFlatOf ∨ c = ⋯.toFlatOf) ↔
    M.Flat F₀ ∧ M.Flat F₁ ∧ F₀ ⊂ F₁ ∧ ∀ (F : Set α), M.Flat F → F₀ ⊆ F → F ⊆ F₁ → F = F₀ ∨ F = F₁
case refine_1
α : Type u_1
M : Matroid α
I F✝ X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e f : α
x✝ :
  ∃ (h : M.Flat F₀) (h_1 : M.Flat F₁),
    ⋯.toFlatOf < ⋯.toFlatOf ∧ ∀ (c : FlatOf M), ⋯.toFlatOf ≤ c → c ≤ ⋯.toFlatOf → c = ⋯.toFlatOf ∨ c = ⋯.toFlatOf
h₀ : M.Flat F₀
h₁ : M.Flat F₁
hlt : ⋯.toFlatOf < ⋯.toFlatOf
hforall : ∀ (c : FlatOf M), ⋯.toFlatOf ≤ c → c ≤ ⋯.toFlatOf → c = ⋯.toFlatOf ∨ c = ⋯.toFlatOf
F : Set α
hF : M.Flat F
hF₀ : F₀ ⊆ F
hF₁ : F ⊆ F₁
⊢ F = F₀ ∨ F = F₁

case refine_2
α : Type u_1
M : Matroid α
I F X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e f : α
x✝ : M.Flat F₀ ∧ M.Flat F₁ ∧ F₀ ⊂ F₁ ∧ ∀ (F : Set α), M.Flat F → F₀ ⊆ F → F ⊆ F₁ → F = F₀ ∨ F = F₁
hF₀ : M.Flat F₀
hF₁ : M.Flat F₁
hss : F₀ ⊂ F₁
hforall : ∀ (F : Set α), M.Flat F → F₀ ⊆ F → F ⊆ F₁ → F = F₀ ∨ F = F₁
⊢ ∀ (c : FlatOf M), ⋯.toFlatOf ≤ c → c ≤ ⋯.toFlatOf → c = ⋯.toFlatOf ∨ c = ⋯.toFlatOf