Theorem: Matroid.ModularPair.symm (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.ModularPair X Y
⊢ M.ModularPair Y X
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
B : Set α
hB : M.ModularBase B fun i => bif i then X else Y
⊢ M.ModularPair Y X

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
B : Set α
hB : M.ModularBase B fun i => bif i then X else Y
⊢ M.ModularPair Y X
Tactic:
exact ⟨B, hB.base, fun i ↦ by simpa using hB.2 !i⟩
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
B : Set α
hB : M.ModularBase B fun i => bif i then X else Y
i : Bool
⊢ M.Basis ((fun i => bif i then Y else X) i ∩ B) ((fun i => bif i then Y else X) i)
Tactic:
simpa using hB.2 !i
State after:
no goals