Theorem: Matroid.ModularPair.inter_cl_eq (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.ModularPair X Y
⊢ M.cl (X ∩ Y) = M.cl X ∩ M.cl Y
Tactic:
convert (ModularFamily.iInter_cl_eq_cl_iInter h).symm
State after:
case h.e'_2.h.e'_3
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.ModularPair X Y
⊢ X ∩ Y = ⋂ i, bif i then X else Y

case h.e'_3
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.ModularPair X Y
⊢ M.cl X ∩ M.cl Y = ⋂ i, M.cl (bif i then X else Y)

State before:
case h.e'_3
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.ModularPair X Y
⊢ M.cl X ∩ M.cl Y = ⋂ i, M.cl (bif i then X else Y)
Tactic:
simp_rw [Bool.cond_eq_ite, apply_ite, ← Bool.cond_eq_ite, inter_eq_iInter]
State after:
no goals

State before:
case h.e'_2.h.e'_3
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.ModularPair X Y
⊢ X ∩ Y = ⋂ i, bif i then X else Y
Tactic:
rw [inter_eq_iInter]
State after:
no goals