Theorem: Matroid.cl_iInter_eq_iInter_cl_of_iUnion_indep (Matroid/Closure.lean)

State before:
α : Type u_1
ι✝ : Type u_2
M : Matroid α
F I J X Y B C R : Set α
e f x y : α
ι : Type u_3
hι : Nonempty ι
Is : ι → Set α
h : M.Indep (⋃ i, Is i)
⊢ M.cl (⋂ i, Is i) = ⋂ i, M.cl (Is i)
Tactic:
convert h.cl_sInter_eq_biInter_cl_of_forall_subset (range_nonempty Is) (by simp [subset_iUnion])
State after:
case h.e'_3
α : Type u_1
ι✝ : Type u_2
M : Matroid α
F I J X Y B C R : Set α
e f x y : α
ι : Type u_3
hι : Nonempty ι
Is : ι → Set α
h : M.Indep (⋃ i, Is i)
⊢ ⋂ i, M.cl (Is i) = ⋂ J ∈ range Is, M.cl J

State before:
case h.e'_3
α : Type u_1
ι✝ : Type u_2
M : Matroid α
F I J X Y B C R : Set α
e f x y : α
ι : Type u_3
hι : Nonempty ι
Is : ι → Set α
h : M.Indep (⋃ i, Is i)
⊢ ⋂ i, M.cl (Is i) = ⋂ J ∈ range Is, M.cl J
Tactic:
simp
State after:
no goals

State before:
α : Type u_1
ι✝ : Type u_2
M : Matroid α
F I J X Y B C R : Set α
e f x y : α
ι : Type u_3
hι : Nonempty ι
Is : ι → Set α
h : M.Indep (⋃ i, Is i)
⊢ ∀ J ∈ range Is, J ⊆ ⋃ i, Is i
Tactic:
simp [subset_iUnion]
State after:
no goals