Module: Mathlib.Combinatorics.SimpleGraph.Extremal.Zarankiewicz

Goal state before:
pp: case refine_1
m n s t : ℕ
V : Type u_1
W : Type u_2
α : Type u_3
β : Type u_4
inst✝³ : Fintype V
inst✝² : Fintype W
inst✝¹ : Fintype α
inst✝ : Fintype β
hm : Fintype.card V = m
hn : Fintype.card W = n
hs : Fintype.card α = s
ht : Fintype.card β = t
e₁ : completeBipartiteGraph V W ≃g completeBipartiteGraph (Fin m) (Fin n) :=
  completeBipartiteGraphCongr (Fintype.equivFinOfCardEq hm) (Fintype.equivFinOfCardEq hn)
K : SimpleGraph (Fin s ⊕ Fin t) := completeBipartiteGraph (Fin s) (Fin t)
e₂ : completeBipartiteGraph α β ≃g completeBipartiteGraph (Fin s) (Fin t) :=
  completeBipartiteGraphCongr (Fintype.equivFinOfCardEq hs) (Fintype.equivFinOfCardEq ht)
⊢ ({G | G ≤ completeBipartiteGraph (Fin m) (Fin n) ∧ (completeBipartiteGraph (Fin s) (Fin t)).Free G}.sup fun x ↦
      #x.edgeFinset) ≤
    {G | G ≤ completeBipartiteGraph V W ∧ (completeBipartiteGraph α β).Free G}.sup fun x ↦ #x.edgeFinset

pp: case refine_2
m n s t : ℕ
V : Type u_1
W : Type u_2
α : Type u_3
β : Type u_4
inst✝³ : Fintype V
inst✝² : Fintype W
inst✝¹ : Fintype α
inst✝ : Fintype β
hm : Fintype.card V = m
hn : Fintype.card W = n
hs : Fintype.card α = s
ht : Fintype.card β = t
e₁ : completeBipartiteGraph V W ≃g completeBipartiteGraph (Fin m) (Fin n) :=
  completeBipartiteGraphCongr (Fintype.equivFinOfCardEq hm) (Fintype.equivFinOfCardEq hn)
K : SimpleGraph (Fin s ⊕ Fin t) := completeBipartiteGraph (Fin s) (Fin t)
e₂ : completeBipartiteGraph α β ≃g completeBipartiteGraph (Fin s) (Fin t) :=
  completeBipartiteGraphCongr (Fintype.equivFinOfCardEq hs) (Fintype.equivFinOfCardEq ht)
⊢ ({G | G ≤ completeBipartiteGraph V W ∧ (completeBipartiteGraph α β).Free G}.sup fun x ↦ #x.edgeFinset) ≤
    {G | G ≤ completeBipartiteGraph (Fin m) (Fin n) ∧ (completeBipartiteGraph (Fin s) (Fin t)).Free G}.sup fun x ↦
      #x.edgeFinset

Tactic:
on_goal 1 =>
    let e₁ := e₁.symm
    let K := completeBipartiteGraph α β
    let e₂ := e₂.symm

Goal state after:
case refine_1
m n s t : ℕ
V : Type u_1
W : Type u_2
α : Type u_3
β : Type u_4
inst✝³ : Fintype V
inst✝² : Fintype W
inst✝¹ : Fintype α
inst✝ : Fintype β
hm : Fintype.card V = m
hn : Fintype.card W = n
hs : Fintype.card α = s
ht : Fintype.card β = t
e₁✝ : completeBipartiteGraph V W ≃g completeBipartiteGraph (Fin m) (Fin n) :=
  completeBipartiteGraphCongr (Fintype.equivFinOfCardEq hm) (Fintype.equivFinOfCardEq hn)
K✝ : SimpleGraph (Fin s ⊕ Fin t) := completeBipartiteGraph (Fin s) (Fin t)
e₂✝ : completeBipartiteGraph α β ≃g completeBipartiteGraph (Fin s) (Fin t) :=
  completeBipartiteGraphCongr (Fintype.equivFinOfCardEq hs) (Fintype.equivFinOfCardEq ht)
e₁ : completeBipartiteGraph (Fin m) (Fin n) ≃g completeBipartiteGraph V W := e₁✝.symm
K : SimpleGraph (α ⊕ β) := completeBipartiteGraph α β
e₂ : completeBipartiteGraph (Fin s) (Fin t) ≃g completeBipartiteGraph α β := e₂✝.symm
⊢ ({G | G ≤ completeBipartiteGraph (Fin m) (Fin n) ∧ (completeBipartiteGraph (Fin s) (Fin t)).Free G}.sup fun x ↦
      #x.edgeFinset) ≤
    {G | G ≤ completeBipartiteGraph V W ∧ (completeBipartiteGraph α β).Free G}.sup fun x ↦ #x.edgeFinset

case refine_2
m n s t : ℕ
V : Type u_1
W : Type u_2
α : Type u_3
β : Type u_4
inst✝³ : Fintype V
inst✝² : Fintype W
inst✝¹ : Fintype α
inst✝ : Fintype β
hm : Fintype.card V = m
hn : Fintype.card W = n
hs : Fintype.card α = s
ht : Fintype.card β = t
e₁ : completeBipartiteGraph V W ≃g completeBipartiteGraph (Fin m) (Fin n) :=
  completeBipartiteGraphCongr (Fintype.equivFinOfCardEq hm) (Fintype.equivFinOfCardEq hn)
K : SimpleGraph (Fin s ⊕ Fin t) := completeBipartiteGraph (Fin s) (Fin t)
e₂ : completeBipartiteGraph α β ≃g completeBipartiteGraph (Fin s) (Fin t) :=
  completeBipartiteGraphCongr (Fintype.equivFinOfCardEq hs) (Fintype.equivFinOfCardEq ht)
⊢ ({G | G ≤ completeBipartiteGraph V W ∧ (completeBipartiteGraph α β).Free G}.sup fun x ↦ #x.edgeFinset) ≤
    {G | G ≤ completeBipartiteGraph (Fin m) (Fin n) ∧ (completeBipartiteGraph (Fin s) (Fin t)).Free G}.sup fun x ↦
      #x.edgeFinset