Theorem: Graph.lift_of_proj (GroupComp/Graph/Covering.lean)

State before:
V : Type u
E : Type v
V₁ : Type ?u.140325
E₁ : Type ?u.140324
V₂ : Type ?u.140329
E₂ : Type ?u.140328
G₁ : Graph V₁ E₁
G₂ : Graph V₂ E₂
p : Morphism G₁ G₂
inst✝ : CoveringMap p
v₁ w₁ : V₁
e : EdgePath G₁ v₁ w₁
⊢ List.map p.toFuncE (toList e) = toList (EdgePath.map e p)
Tactic:
simp [map_toList]
State after:
no goals

State before:
V : Type u
E : Type v
V₁ : Type u_1
E₁ : Type u_2
V₂ : Type u_3
E₂ : Type u_4
G₁ : Graph V₁ E₁
G₂ : Graph V₂ E₂
p : Morphism G₁ G₂
inst✝ : CoveringMap p
v₁ w₁ : V₁
e : EdgePath G₁ v₁ w₁
⊢ lift (EdgePath.map e p) p v₁ (_ : p.toFuncV v₁ = p.toFuncV v₁) =
    { τ := w₁, path := e, term_pushdown := (_ : p.toFuncV w₁ = p.toFuncV w₁),
      list_pushdown := (_ : List.map p.toFuncE (toList e) = toList (EdgePath.map e p)) }
Tactic:
apply unique_Pathlift
State after:
no goals