-- Mathlib/.lake/packages/batteries/Batteries/Data/HashMap/WF.lean
theorem WF.filterMap {α β γ} {f : α → β → Option γ} [BEq α] [Hashable α]
    {m : Imp α β} (H : WF m) : WF (filterMap f m)

Proof state:
case refl
α : Type u_1
β : Type u_2
γ : Type u_3
f : α → β → Option γ
inst✝¹ : BEq α
inst✝ : Hashable α
m : Imp α β
H : m.WF
g₁ : AssocList α β → List (α × γ) :=
  fun l => List.filterMap (fun x => Option.map (fun x_1 => (x.fst, x_1)) (f x.fst x.snd)) l.toList
H1 :
  ∀ (l : AssocList α β) (n : ULift Nat) (acc : AssocList α γ),
    filterMap.go f acc l n = (((g₁ l).reverse ++ acc.toList).toAssocList, { down := n.down + (g₁ l).length })
g : AssocList α β → AssocList α γ := fun l => (g₁ l).reverse.toAssocList
M : Type (max u_3 u_1) → Type (max u_3 u_1) := StateT (ULift Nat) Id
H2 :
  ∀ (l : List (AssocList α β)) (n : ULift Nat),
    List.mapM (filterMap.go f AssocList.nil) l n =
      (List.map g l, { down := n.down + (List.map (fun x => x.toList.length) (List.map g l)).sum })
H3 :
  ∀ (l : List (α × β)),
    (List.map (fun a => a.fst)
          (List.filterMap
            (fun x =>
              match x with
              | (a, b) => Option.map (fun x => (a, x)) (f a b))
            l)).Sublist
      (List.map (fun x => x.fst) l)
h :
  0 <
    (List.map (fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList,
          {
            down :=
              (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList)
                  m.buckets.val.toList).sum }).fst.length
⊢ { size := (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList).sum,
      buckets :=
        ⟨{
            toList :=
              (List.map (fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList,
                  {
                    down :=
                      (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList)
                          m.buckets.val.toList).sum }).fst },
          h⟩ }.WF

Tactic:
refine .mk (by simp [Buckets.size]) ⟨?_, fun i h => ?_⟩

Result:
case refl.refine_1
α : Type u_1
β : Type u_2
γ : Type u_3
f : α → β → Option γ
inst✝¹ : BEq α
inst✝ : Hashable α
m : Imp α β
H : m.WF
g₁ : AssocList α β → List (α × γ) :=
  fun l => List.filterMap (fun x => Option.map (fun x_1 => (x.fst, x_1)) (f x.fst x.snd)) l.toList
H1 :
  ∀ (l : AssocList α β) (n : ULift Nat) (acc : AssocList α γ),
    filterMap.go f acc l n = (((g₁ l).reverse ++ acc.toList).toAssocList, { down := n.down + (g₁ l).length })
g : AssocList α β → AssocList α γ := fun l => (g₁ l).reverse.toAssocList
M : Type (max u_3 u_1) → Type (max u_3 u_1) := StateT (ULift Nat) Id
H2 :
  ∀ (l : List (AssocList α β)) (n : ULift Nat),
    List.mapM (filterMap.go f AssocList.nil) l n =
      (List.map g l, { down := n.down + (List.map (fun x => x.toList.length) (List.map g l)).sum })
H3 :
  ∀ (l : List (α × β)),
    (List.map (fun a => a.fst)
          (List.filterMap
            (fun x =>
              match x with
              | (a, b) => Option.map (fun x => (a, x)) (f a b))
            l)).Sublist
      (List.map (fun x => x.fst) l)
h :
  0 <
    (List.map (fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList,
          {
            down :=
              (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList)
                  m.buckets.val.toList).sum }).fst.length
⊢ ∀ [inst : LawfulHashable α] [inst : PartialEquivBEq α] (bucket : AssocList α γ),
    bucket ∈
        {
                size :=
                  (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList)
                      m.buckets.val.toList).sum,
                buckets :=
                  ⟨{
                      toList :=
                        (List.map (fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList,
                            {
                              down :=
                                (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList)
                                    m.buckets.val.toList).sum }).fst },
                    h⟩ }.buckets.val.toList →
      List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) bucket.toList

case refl.refine_2
α : Type u_1
β : Type u_2
γ : Type u_3
f : α → β → Option γ
inst✝¹ : BEq α
inst✝ : Hashable α
m : Imp α β
H : m.WF
g₁ : AssocList α β → List (α × γ) :=
  fun l => List.filterMap (fun x => Option.map (fun x_1 => (x.fst, x_1)) (f x.fst x.snd)) l.toList
H1 :
  ∀ (l : AssocList α β) (n : ULift Nat) (acc : AssocList α γ),
    filterMap.go f acc l n = (((g₁ l).reverse ++ acc.toList).toAssocList, { down := n.down + (g₁ l).length })
g : AssocList α β → AssocList α γ := fun l => (g₁ l).reverse.toAssocList
M : Type (max u_3 u_1) → Type (max u_3 u_1) := StateT (ULift Nat) Id
H2 :
  ∀ (l : List (AssocList α β)) (n : ULift Nat),
    List.mapM (filterMap.go f AssocList.nil) l n =
      (List.map g l, { down := n.down + (List.map (fun x => x.toList.length) (List.map g l)).sum })
H3 :
  ∀ (l : List (α × β)),
    (List.map (fun a => a.fst)
          (List.filterMap
            (fun x =>
              match x with
              | (a, b) => Option.map (fun x => (a, x)) (f a b))
            l)).Sublist
      (List.map (fun x => x.fst) l)
h✝ :
  0 <
    (List.map (fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList,
          {
            down :=
              (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList)
                  m.buckets.val.toList).sum }).fst.length
i : Nat
h :
  i <
    { size := (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList).sum,
            buckets :=
              ⟨{
                  toList :=
                    (List.map (fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList,
                        {
                          down :=
                            (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList)
                                m.buckets.val.toList).sum }).fst },
                h✝⟩ }.buckets.val.size
⊢ AssocList.All
    (fun k x =>
      ((hash k).toUSize %
            USize.ofNat
              {
                      size :=
                        (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList)
                            m.buckets.val.toList).sum,
                      buckets :=
                        ⟨{
                            toList :=
                              (List.map (fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList,
                                  {
                                    down :=
                                      (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList)
                                          m.buckets.val.toList).sum }).fst },
                          h✝⟩ }.buckets.val.size).toNat =
        i)
    { size := (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList).sum,
            buckets :=
              ⟨{
                  toList :=
                    (List.map (fun l => (g₁ l).reverse.toAssocList) m.buckets.val.toList,
                        {
                          down :=
                            (List.map ((fun x => x.toList.length) ∘ fun l => (g₁ l).reverse.toAssocList)
                                m.buckets.val.toList).sum }).fst },
                h✝⟩ }.buckets.val[i]