Theorem: Matroid.ModularFamily.modularPair_singleton_compl_biInter (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
inst✝ : Nontrivial ι
h : M.ModularFamily Xs
i₀ : ι
⊢ M.ModularPair (Xs i₀) (⋂ i ∈ {i₀}ᶜ, Xs i)
Tactic:
convert h.modularPair_compl_biInter {i₀} (by simp)
  (by simpa [ne_univ_iff_exists_not_mem, mem_singleton_iff] using exists_ne i₀)
State after:
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
inst✝ : Nontrivial ι
h : M.ModularFamily Xs
i₀ : ι
⊢ Xs i₀ = ⋂ i ∈ {i₀}, Xs i

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
inst✝ : Nontrivial ι
h : M.ModularFamily Xs
i₀ : ι
⊢ Xs i₀ = ⋂ i ∈ {i₀}, Xs i
Tactic:
simp
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
inst✝ : Nontrivial ι
h : M.ModularFamily Xs
i₀ : ι
⊢ {i₀}.Nonempty
Tactic:
simp
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
inst✝ : Nontrivial ι
h : M.ModularFamily Xs
i₀ : ι
⊢ {i₀} ≠ univ
Tactic:
simpa [ne_univ_iff_exists_not_mem, mem_singleton_iff] using exists_ne i₀
State after:
no goals