Theorem: Matroid.Flat.sInter (Matroid/Flat.lean)

State before:
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
Fs : Set (Set α)
hF : Fs.Nonempty
h : ∀ F ∈ Fs, M.Flat F
⊢ M.Flat (⋂₀ Fs)
Tactic:
rw [sInter_eq_iInter]
State after:
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
Fs : Set (Set α)
hF : Fs.Nonempty
h : ∀ F ∈ Fs, M.Flat F
⊢ M.Flat (⋂ i, ↑i)

State before:
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
Fs : Set (Set α)
hF : Fs.Nonempty
h : ∀ F ∈ Fs, M.Flat F
⊢ M.Flat (⋂ i, ↑i)
Tactic:
have : Nonempty Fs := Iff.mpr nonempty_coe_sort hF
State after:
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
Fs : Set (Set α)
hF : Fs.Nonempty
h : ∀ F ∈ Fs, M.Flat F
this : Nonempty ↑Fs
⊢ M.Flat (⋂ i, ↑i)

State before:
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
Fs : Set (Set α)
hF : Fs.Nonempty
h : ∀ F ∈ Fs, M.Flat F
this : Nonempty ↑Fs
⊢ M.Flat (⋂ i, ↑i)
Tactic:
exact Flat.iInter (fun ⟨F, hF⟩ ↦ h _ hF)
State after:
no goals