Theorem: Matroid.ModularFamily.ofRestrict (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
M : Matroid α
R : Set α
hR : R ⊆ M.E
h : (M ↾ R).ModularFamily Xs
⊢ M.ModularFamily Xs
Tactic:
convert h.ofRestrict' with i
State after:
case h.e'_4.h
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
M : Matroid α
R : Set α
hR : R ⊆ M.E
h : (M ↾ R).ModularFamily Xs
i : ι
⊢ Xs i = Xs i ∩ M.E

State before:
case h.e'_4.h
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
M : Matroid α
R : Set α
hR : R ⊆ M.E
h : (M ↾ R).ModularFamily Xs
i : ι
⊢ Xs i = Xs i ∩ M.E
Tactic:
rw [inter_eq_self_of_subset_left <| (h.subset_ground_of_mem i).trans hR]
State after:
no goals