Theorem: Matroid.Nonloop.exists_mem_cocircuit (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
he : M.Nonloop e
⊢ ∃ K, M.Cocircuit K ∧ e ∈ K
Tactic:
obtain ⟨B, hB, heB⟩ := he.exists_mem_base
State after:
case intro.intro
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
he : M.Nonloop e
B : Set α
hB : M.Base B
heB : e ∈ B
⊢ ∃ K, M.Cocircuit K ∧ e ∈ K

State before:
case intro.intro
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
he : M.Nonloop e
B : Set α
hB : M.Base B
heB : e ∈ B
⊢ ∃ K, M.Cocircuit K ∧ e ∈ K
Tactic:
exact ⟨_, fundCocct_cocircuit heB hB, mem_fundCocct M e B⟩
State after:
no goals