Theorem: Matroid.Point.subset_or_inter_eq_loops_of_flat (Matroid/Flat.lean)

State before:
α : Type u_1
M : Matroid α
I F X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e f : α
hP : M.Point P
hF : M.Flat F
⊢ P ⊆ F ∨ P ∩ F = M.cl ∅
Tactic:
obtain (h | h) := hP.eq_or_eq_of_flat_of_subset (hP.flat.inter hF) inter_subset_left
State after:
case inl
α : Type u_1
M : Matroid α
I F X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e f : α
hP : M.Point P
hF : M.Flat F
h : P ∩ F = M.cl ∅
⊢ P ⊆ F ∨ P ∩ F = M.cl ∅

case inr
α : Type u_1
M : Matroid α
I F X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e f : α
hP : M.Point P
hF : M.Flat F
h : P ∩ F = P
⊢ P ⊆ F ∨ P ∩ F = M.cl ∅

State before:
case inr
α : Type u_1
M : Matroid α
I F X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e f : α
hP : M.Point P
hF : M.Flat F
h : P ∩ F = P
⊢ P ⊆ F ∨ P ∩ F = M.cl ∅
Tactic:
exact Or.inl (inter_eq_left.1 h)
State after:
no goals

State before:
case inl
α : Type u_1
M : Matroid α
I F X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e f : α
hP : M.Point P
hF : M.Flat F
h : P ∩ F = M.cl ∅
⊢ P ⊆ F ∨ P ∩ F = M.cl ∅
Tactic:
exact Or.inr h
State after:
no goals