Theorem: Matroid.ModularFamily.comp (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
η : Type u_3
h : M.ModularFamily Xs
t : η → ι
⊢ M.ModularFamily (Xs ∘ t)
Tactic:
obtain ⟨B, hB, hBXs⟩ := h
State after:
case intro.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
η : Type u_3
t : η → ι
B : Set α
hB : M.Base B
hBXs : ∀ (i : ι), M.Basis (Xs i ∩ B) (Xs i)
⊢ M.ModularFamily (Xs ∘ t)

State before:
case intro.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
η : Type u_3
t : η → ι
B : Set α
hB : M.Base B
hBXs : ∀ (i : ι), M.Basis (Xs i ∩ B) (Xs i)
⊢ M.ModularFamily (Xs ∘ t)
Tactic:
exact ⟨B, hB, fun i ↦ (by simpa using hBXs (t 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
η : Type u_3
t : η → ι
B : Set α
hB : M.Base B
hBXs : ∀ (i : ι), M.Basis (Xs i ∩ B) (Xs i)
i : η
⊢ M.Basis ((Xs ∘ t) i ∩ B) ((Xs ∘ t) i)
Tactic:
simpa using hBXs (t i)
State after:
no goals