Theorem: Matroid.Indep.skew_iff_disjoint_union_indep (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
hI : M.Indep I
hJ : M.Indep J
⊢ M.Skew I J ↔ Disjoint I J ∧ M.Indep (I ∪ J)
Tactic:
refine ⟨fun h ↦ ⟨h.disjoint_of_indep_left hI, ?_⟩, fun h ↦ h.2.skew_iff_disjoint.2 h.1⟩
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
hI : M.Indep I
hJ : M.Indep J
h : M.Skew I J
⊢ M.Indep (I ∪ J)

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
hI : M.Indep I
hJ : M.Indep J
h : M.Skew I J
⊢ M.Indep (I ∪ J)
Tactic:
exact h.union_indep_of_indep_subsets hI Subset.rfl hJ Subset.rfl
State after:
no goals