Theorem: Matroid.SkewFamily.iUnion_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.SkewFamily Xs
hIs : ∀ (i : ι), M.Basis (Is i) (Xs i)
⊢ M.Basis (⋃ i, Is i) (⋃ i, Xs i)
Tactic:
have hi := h.iUnion_indep_subset_indep (fun i ↦ (hIs i).subset) (fun i ↦ (hIs i).indep)
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.SkewFamily Xs
hIs : ∀ (i : ι), M.Basis (Is i) (Xs i)
hi : M.Indep (⋃ i, Is i)
⊢ M.Basis (⋃ i, Is i) (⋃ i, Xs i)

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.SkewFamily Xs
hIs : ∀ (i : ι), M.Basis (Is i) (Xs i)
hi : M.Indep (⋃ i, Is i)
⊢ M.Basis (⋃ i, Is i) (⋃ i, Xs i)
Tactic:
exact hi.basis_of_subset_of_subset_cl (iUnion_mono (fun i ↦ (hIs i).subset)) <|
  iUnion_subset (fun i ↦ (hIs i).subset_cl.trans (M.cl_subset_cl (subset_iUnion _ _)))
State after:
no goals