Theorem: Matroid.restriction_loop_iff (Matroid/Loop.lean)

State before:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
hNM : N ≤r M
⊢ N.Loop e ↔ e ∈ N.E ∧ M.Loop e
Tactic:
obtain ⟨R, hR, rfl⟩ := hNM
State after:
case intro.intro
α : Type u_1
β : Type u_2
M : Matroid α
e f : α
B L L' I X Y Z F C K R : Set α
hR : R ⊆ M.E
⊢ (M ↾ R).Loop e ↔ e ∈ (M ↾ R).E ∧ M.Loop e

State before:
case intro.intro
α : Type u_1
β : Type u_2
M : Matroid α
e f : α
B L L' I X Y Z F C K R : Set α
hR : R ⊆ M.E
⊢ (M ↾ R).Loop e ↔ e ∈ (M ↾ R).E ∧ M.Loop e
Tactic:
simp only [restrict_loop_iff, restrict_ground_eq, and_congr_right_iff, or_iff_left_iff_imp]
State after:
case intro.intro
α : Type u_1
β : Type u_2
M : Matroid α
e f : α
B L L' I X Y Z F C K R : Set α
hR : R ⊆ M.E
⊢ e ∈ R → e ∉ M.E → M.Loop e

State before:
case intro.intro
α : Type u_1
β : Type u_2
M : Matroid α
e f : α
B L L' I X Y Z F C K R : Set α
hR : R ⊆ M.E
⊢ e ∈ R → e ∉ M.E → M.Loop e
Tactic:
exact fun heR heE ↦ (heE (hR heR)).elim
State after:
no goals