Theorem: Matroid.SkewFamily.disjoint_inter_indep (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
hI : M.Indep I
hij : i ≠ j
⊢ Disjoint (Xs i ∩ I) (Xs j)
Tactic:
rw [disjoint_iff_forall_ne]
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
hI : M.Indep I
hij : i ≠ j
⊢ ∀ ⦃a : α⦄, a ∈ Xs i ∩ I → ∀ ⦃b : α⦄, b ∈ Xs j → a ≠ b

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
hI : M.Indep I
hij : i ≠ j
⊢ ∀ ⦃a : α⦄, a ∈ Xs i ∩ I → ∀ ⦃b : α⦄, b ∈ Xs j → a ≠ b
Tactic:
rintro e ⟨hei, heI⟩ _ hej rfl
State after:
case intro
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
hI : M.Indep I
hij : i ≠ j
e : α
hei : e ∈ Xs i
heI : e ∈ I
hej : e ∈ Xs j
⊢ False

State before:
case intro
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
hI : M.Indep I
hij : i ≠ j
e : α
hei : e ∈ Xs i
heI : e ∈ I
hej : e ∈ Xs j
⊢ False
Tactic:
exact (hI.nonloop_of_mem heI).not_loop <| h.loop_of_mem_inter hij ⟨hei,hej⟩
State after:
no goals