Theorem: Matroid.skew_iff_modularPair_inter_subset_loops (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.Skew X Y ↔ M.ModularPair X Y ∧ X ∩ Y ⊆ M.cl ∅
Tactic:
rw [Skew, SkewFamily, ModularPair, and_congr_right_iff]
State after:
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.ModularFamily fun i => bif i then X else Y) →
    ((∀ ⦃i j : Bool⦄, i ≠ j → ((bif i then X else Y) ∩ bif j then X else Y) ⊆ M.cl ∅) ↔ X ∩ Y ⊆ M.cl ∅)

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.ModularFamily fun i => bif i then X else Y) →
    ((∀ ⦃i j : Bool⦄, i ≠ j → ((bif i then X else Y) ∩ bif j then X else Y) ⊆ M.cl ∅) ↔ X ∩ Y ⊆ M.cl ∅)
Tactic:
simp [inter_comm X Y]
State after:
no goals