Theorem: Matroid.CovBy.exists_eq_cl_insert' (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
h : M.cl X ⋖[M] F
⊢ ∃ e ∈ F \ M.cl X, F = M.cl (insert e X)
Tactic:
obtain ⟨e, he, rfl⟩ := h.exists_eq_cl_insert
State after:
case intro.intro
α : Type u_1
M : Matroid α
I X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e✝ f e : α
h : M.cl X ⋖[M] M.cl (insert e (M.cl X))
he : e ∈ M.cl (insert e (M.cl X)) \ M.cl X
⊢ ∃ e_1 ∈ M.cl (insert e (M.cl X)) \ M.cl X, M.cl (insert e (M.cl X)) = M.cl (insert e_1 X)

State before:
case intro.intro
α : Type u_1
M : Matroid α
I X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e✝ f e : α
h : M.cl X ⋖[M] M.cl (insert e (M.cl X))
he : e ∈ M.cl (insert e (M.cl X)) \ M.cl X
⊢ ∃ e_1 ∈ M.cl (insert e (M.cl X)) \ M.cl X, M.cl (insert e (M.cl X)) = M.cl (insert e_1 X)
Tactic:
exact ⟨e, he, by simp⟩
State after:
no goals

State before:
α : Type u_1
M : Matroid α
I X Y F' F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e✝ f e : α
h : M.cl X ⋖[M] M.cl (insert e (M.cl X))
he : e ∈ M.cl (insert e (M.cl X)) \ M.cl X
⊢ M.cl (insert e (M.cl X)) = M.cl (insert e X)
Tactic:
simp
State after:
no goals