Theorem: Matroid.ModularBase.basis_iUnion (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
h : M.ModularBase B Xs
⊢ M.Basis ((⋃ i, Xs i) ∩ B) (⋃ i, Xs i)
Tactic:
simp_rw [h.1.indep.inter_basis_cl_iff_subset_cl_inter, iUnion_subset_iff]
State after:
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
h : M.ModularBase B Xs
⊢ ∀ (i : ι), Xs i ⊆ M.cl ((⋃ i, Xs i) ∩ B)

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
h : M.ModularBase B Xs
⊢ ∀ (i : ι), Xs i ⊆ M.cl ((⋃ i, Xs i) ∩ B)
Tactic:
exact fun i ↦ (h.subset_cl_inter i).trans
  (M.cl_subset_cl (inter_subset_inter_left _ (subset_iUnion _ i)))
State after:
no goals