simp only [Prod.mk.eta, Set.mem_toFinset, mem_edgeSet, deleteEdges_adj, Set.mem_singleton_iff]
case insert.hs.a.mk
V : Type u_1
inst✝ : Finite V
motive : Digraph V → Prop
hbot : motive ⊥
hdelete : ∀ (G : Digraph V) (v w : V), G.Adj v w → motive (deleteEdges G {(v, w)}) → motive G
this✝ : Fintype V
e : V × V
s : Finset (V × V)
he : ¬e ∈ s
ih : ∀ (G : Digraph V), Set.toFinset (edgeSet G) = s → motive G
G : Digraph V
hs : Set.toFinset (edgeSet G) = insert e s
this : e ∈ edgeSet G
v w : V
⊢ (v, w) ∈ Set.toFinset (edgeSet (deleteEdges G {(e.fst, e.snd)})) ↔ (v, w) ∈ s
case insert.hs.a.mk
V : Type u_1
inst✝ : Finite V
motive : Digraph V → Prop
hbot : motive ⊥
hdelete : ∀ (G : Digraph V) (v w : V), G.Adj v w → motive (deleteEdges G {(v, w)}) → motive G
this✝ : Fintype V
e : V × V
s : Finset (V × V)
he : ¬e ∈ s
ih : ∀ (G : Digraph V), Set.toFinset (edgeSet G) = s → motive G
G : Digraph V
hs : Set.toFinset (edgeSet G) = insert e s
this : e ∈ edgeSet G
v w : V
⊢ G.Adj v w ∧ ¬(v, w) = e ↔ (v, w) ∈ s