Theorem: Digraph.Path.loop_eq (GraphProjects/DigraphConnectivity.lean)

State before:
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
v : V
p : Path G v v
⊢ p = Path.nil
Tactic:
obtain ⟨_ | _, h⟩ := p
State after:
case mk.nil
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
v : V
h : Walk.IsPath Walk.nil
⊢ { val := Walk.nil, property := h } = Path.nil

case mk.cons
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
v v✝ : V
h✝ : G.Adj v v✝
p✝ : Walk G v✝ v
h : Walk.IsPath (Walk.cons h✝ p✝)
⊢ { val := Walk.cons h✝ p✝, property := h } = Path.nil

State before:
case mk.nil
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
v : V
h : Walk.IsPath Walk.nil
⊢ { val := Walk.nil, property := h } = Path.nil
Tactic:
rfl
State after:
no goals

State before:
case mk.cons
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
v v✝ : V
h✝ : G.Adj v v✝
p✝ : Walk G v✝ v
h : Walk.IsPath (Walk.cons h✝ p✝)
⊢ { val := Walk.cons h✝ p✝, property := h } = Path.nil
Tactic:
simp at h
State after:
no goals