Theorem: Matroid.Indep.subset_skew_diff (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.Indep I
hJI : J ⊆ I
⊢ M.Skew J (I \ J)
Tactic:
rw [Indep.skew_iff_disjoint]
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.Indep I
hJI : J ⊆ I
⊢ Disjoint J (I \ J)

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.Indep I
hJI : J ⊆ I
⊢ M.Indep (J ∪ 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
h : M.Indep I
hJI : J ⊆ I
⊢ M.Indep (J ∪ I \ J)
Tactic:
exact h.subset (union_subset hJI diff_subset)
State after:
no goals

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.Indep I
hJI : J ⊆ I
⊢ Disjoint J (I \ J)
Tactic:
exact disjoint_sdiff_right
State after:
no goals