Theorem: Matroid.Skew.union_basis_union (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.Skew X Y
hI : M.Basis I X
hJ : M.Basis J Y
⊢ M.Basis (I ∪ J) (X ∪ Y)
Tactic:
rw [union_eq_iUnion, union_eq_iUnion]
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.Skew X Y
hI : M.Basis I X
hJ : M.Basis J Y
⊢ M.Basis (⋃ b, bif b then I else J) (⋃ b, bif b then X else Y)

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.Skew X Y
hI : M.Basis I X
hJ : M.Basis J Y
⊢ M.Basis (⋃ b, bif b then I else J) (⋃ b, bif b then X else Y)
Tactic:
exact SkewFamily.iUnion_basis_iUnion h (Bool.rec (by simpa) (by simpa))
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.Skew X Y
hI : M.Basis I X
hJ : M.Basis J Y
⊢ M.Basis (bif false then I else J) (bif false then X else Y)
Tactic:
simpa
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.Skew X Y
hI : M.Basis I X
hJ : M.Basis J Y
⊢ M.Basis (bif true then I else J) (bif true then X else Y)
Tactic:
simpa
State after:
no goals