Theorem: Matroid.SkewFamily.cls_skewFamily (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.SkewFamily Xs
⊢ M.SkewFamily fun i => M.cl (Xs i)
Tactic:
refine ⟨h.modularFamily.cls_modularFamily, fun i j hij ↦ ?_⟩
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.SkewFamily Xs
i j : ι
hij : i ≠ j
⊢ (fun i => M.cl (Xs i)) i ∩ (fun i => M.cl (Xs i)) j ⊆ M.cl ∅

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.SkewFamily Xs
i j : ι
hij : i ≠ j
⊢ (fun i => M.cl (Xs i)) i ∩ (fun i => M.cl (Xs i)) j ⊆ M.cl ∅
Tactic:
have := M.cl_subset_cl_of_subset_cl <| h.subset_loops_of_ne hij
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.SkewFamily Xs
i j : ι
hij : i ≠ j
this : M.cl (Xs i ∩ Xs j) ⊆ M.cl ∅
⊢ (fun i => M.cl (Xs i)) i ∩ (fun i => M.cl (Xs i)) j ⊆ M.cl ∅

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.SkewFamily Xs
i j : ι
hij : i ≠ j
this : M.cl (Xs i ∩ Xs j) ⊆ M.cl ∅
⊢ (fun i => M.cl (Xs i)) i ∩ (fun i => M.cl (Xs i)) j ⊆ M.cl ∅
Tactic:
rwa [← (h.modularFamily.modularPair i j).inter_cl_eq]
State after:
no goals