Theorem: Matroid.ModularFamily.set_biInter_comp (Matroid/Modular.lean)

State before:
ι : Type u_1
α : Type u_2
M : Matroid α
B I J X X' Y Y' F : Set α
Xs Ys Js Is : ι → Set α
i j : ι
e f : α
η : Type u_3
h : M.ModularFamily Xs
t : η → Set ι
ht : ∀ (j : η), (t j).Nonempty
⊢ M.ModularFamily fun j => ⋂ i ∈ t j, Xs i
Tactic:
obtain ⟨B, hB⟩ := h
State after:
case intro
ι : Type u_1
α : Type u_2
M : Matroid α
B✝ I J X X' Y Y' F : Set α
Xs Ys Js Is : ι → Set α
i j : ι
e f : α
η : Type u_3
t : η → Set ι
ht : ∀ (j : η), (t j).Nonempty
B : Set α
hB : M.ModularBase B Xs
⊢ M.ModularFamily fun j => ⋂ i ∈ t j, Xs i

State before:
case intro
ι : Type u_1
α : Type u_2
M : Matroid α
B✝ I J X X' Y Y' F : Set α
Xs Ys Js Is : ι → Set α
i j : ι
e f : α
η : Type u_3
t : η → Set ι
ht : ∀ (j : η), (t j).Nonempty
B : Set α
hB : M.ModularBase B Xs
⊢ M.ModularFamily fun j => ⋂ i ∈ t j, Xs i
Tactic:
exact ⟨B, hB.base, fun j ↦ hB.basis_biInter (ht j)⟩
State after:
no goals