Theorem: Matroid.ModularFamily.modularPair (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.ModularFamily Xs
i j : ι
⊢ M.ModularPair (Xs i) (Xs j)
Tactic:
obtain ⟨B, hB⟩ := h
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
i j : ι
B : Set α
hB : M.ModularBase B Xs
⊢ M.ModularPair (Xs i) (Xs j)

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
i j : ι
B : Set α
hB : M.ModularBase B Xs
⊢ M.ModularPair (Xs i) (Xs j)
Tactic:
exact modularPair_iff.2 ⟨B, hB.indep, hB.basis_inter i, hB.basis_inter j⟩
State after:
no goals