Theorem: Matroid.CovBy.er_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
h : F ⋖[M] F'
⊢ M.er F' = M.er F + 1
Tactic:
obtain ⟨e, he, rfl⟩ := h.exists_eq_cl_insert
State after:
case intro.intro
α : Type u_1
M : Matroid α
I F X Y F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e✝ f e : α
h : F ⋖[M] M.cl (insert e F)
he : e ∈ M.cl (insert e F) \ F
⊢ M.er (M.cl (insert e F)) = M.er F + 1

State before:
case intro.intro
α : Type u_1
M : Matroid α
I F X Y F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e✝ f e : α
h : F ⋖[M] M.cl (insert e F)
he : e ∈ M.cl (insert e F) \ F
⊢ M.er (M.cl (insert e F)) = M.er F + 1
Tactic:
rw [er_cl_eq, h.flat_left.er_insert_eq_add_one]
State after:
case intro.intro
α : Type u_1
M : Matroid α
I F X Y F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e✝ f e : α
h : F ⋖[M] M.cl (insert e F)
he : e ∈ M.cl (insert e F) \ F
⊢ e ∈ M.E \ F

State before:
case intro.intro
α : Type u_1
M : Matroid α
I F X Y F₀ F₁ F₂ P L H H₁ H₂ H' B C K : Set α
e✝ f e : α
h : F ⋖[M] M.cl (insert e F)
he : e ∈ M.cl (insert e F) \ F
⊢ e ∈ M.E \ F
Tactic:
exact ⟨M.cl_subset_ground _ he.1, he.2⟩
State after:
no goals