Theorem: Matroid.exists_mem_circuit_of_not_coloop (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
heE : e ∈ M.E
he : ¬M.Coloop e
⊢ ∃ C, M.Circuit C ∧ e ∈ C
Tactic:
simp only [coloop_iff_forall_mem_base, not_forall, Classical.not_imp, exists_prop] at he
State after:
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
heE : e ∈ M.E
he : ∃ x, M.Base x ∧ e ∉ x
⊢ ∃ C, M.Circuit C ∧ e ∈ C

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
heE : e ∈ M.E
he : ∃ x, M.Base x ∧ e ∉ x
⊢ ∃ C, M.Circuit C ∧ e ∈ C
Tactic:
obtain ⟨B, hB, heB⟩ := he
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
heE : e ∈ M.E
B : Set α
hB : M.Base B
heB : e ∉ B
⊢ ∃ C, M.Circuit C ∧ e ∈ C

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
heE : e ∈ M.E
B : Set α
hB : M.Base B
heB : e ∉ B
⊢ ∃ C, M.Circuit C ∧ e ∈ C
Tactic:
exact ⟨M.fundCct e B, hB.fundCct_circuit ⟨heE,heB⟩, .inl rfl⟩
State after:
no goals