Theorem: Matroid.Flat.wCovby_iff_covBy_or_eq (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
hF₀ : M.Flat F₀
hF₁ : M.Flat F₁
⊢ F₀ ⩿[M] F₁ ↔ (F₀ ⋖[M] F₁) ∨ F₀ = F₁
Tactic:
obtain (rfl | hne) := eq_or_ne F₀ F₁
State after:
case inl
α : Type u_1
M : Matroid α
I F X Y F' F₀ F₂ P L H H₁ H₂ H' B C K : Set α
e f : α
hF₀ hF₁ : M.Flat F₀
⊢ F₀ ⩿[M] F₀ ↔ (F₀ ⋖[M] F₀) ∨ F₀ = F₀

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
hF₀ : M.Flat F₀
hF₁ : M.Flat F₁
hne : F₀ ≠ F₁
⊢ F₀ ⩿[M] F₁ ↔ (F₀ ⋖[M] F₁) ∨ F₀ = F₁

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
hF₀ : M.Flat F₀
hF₁ : M.Flat F₁
hne : F₀ ≠ F₁
⊢ F₀ ⩿[M] F₁ ↔ (F₀ ⋖[M] F₁) ∨ F₀ = F₁
Tactic:
simp [hF₀, hF₀.covBy_iff_wcovBy_and_ne hF₁, or_iff_not_imp_right, hne]
State after:
no goals

State before:
case inl
α : Type u_1
M : Matroid α
I F X Y F' F₀ F₂ P L H H₁ H₂ H' B C K : Set α
e f : α
hF₀ hF₁ : M.Flat F₀
⊢ F₀ ⩿[M] F₀ ↔ (F₀ ⋖[M] F₀) ∨ F₀ = F₀
Tactic:
simp [hF₀]
State after:
no goals