-- Mathlib/.lake/packages/lean4/src/lean/Std/Data/DHashMap/Internal/Model.lean
theorem containsThenInsert_eq_containsₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α) (b : β a) :
    (m.containsThenInsert a b).1 = m.containsₘ a

Proof state:
α : Type u
β : α → Type v
inst✝¹ : BEq α
inst✝ : Hashable α
m : Raw₀ α β
a : α
b : β a
⊢ (match mkIdx m.1.buckets.size ⋯ (hash a) with
      | ⟨i, h⟩ =>
        let bkt := m.1.buckets[i];
        if AssocList.contains a bkt = true then
          let buckets' := m.1.buckets.uset i AssocList.nil h;
          (true, ⟨{ size := m.1.size, buckets := buckets'.uset i (AssocList.replace a b bkt) ⋯ }, ⋯⟩)
        else
          let size' := m.1.size + 1;
          let buckets' := m.1.buckets.uset i (AssocList.cons a b bkt) h;
          (false, expandIfNecessary ⟨{ size := size', buckets := buckets' }, ⋯⟩)).fst =
    AssocList.contains a
      (match mkIdx m.val.buckets.size ⋯ (hash a) with
      | ⟨i, h⟩ => m.val.buckets[i])

Tactic:
dsimp only [Array.ugetElem_eq_getElem, Array.uset]

Result:
α : Type u
β : α → Type v
inst✝¹ : BEq α
inst✝ : Hashable α
m : Raw₀ α β
a : α
b : β a
⊢ (if AssocList.contains a m.1.buckets[(mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat] = true then
        (true,
          ⟨{ size := m.1.size,
              buckets :=
                (m.1.buckets.set (mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat AssocList.nil ⋯).set
                  (mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat
                  (AssocList.replace a b m.1.buckets[(mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat]) ⋯ },
            ⋯⟩)
      else
        (false,
          expandIfNecessary
            ⟨{ size := m.1.size + 1,
                buckets :=
                  m.1.buckets.set (mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat
                    (AssocList.cons a b m.1.buckets[(mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat]) ⋯ },
              ⋯⟩)).fst =
    AssocList.contains a m.val.buckets[(mkIdx m.val.buckets.size ⋯ (hash a)).val.toNat]

Proof state:
α : Type u
β : α → Type v
inst✝¹ : BEq α
inst✝ : Hashable α
m : Raw₀ α β
a : α
b : β a
⊢ (if AssocList.contains a m.1.buckets[(mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat] = true then
        (true,
          ⟨{ size := m.1.size,
              buckets :=
                (m.1.buckets.set (mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat AssocList.nil ⋯).set
                  (mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat
                  (AssocList.replace a b m.1.buckets[(mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat]) ⋯ },
            ⋯⟩)
      else
        (false,
          expandIfNecessary
            ⟨{ size := m.1.size + 1,
                buckets :=
                  m.1.buckets.set (mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat
                    (AssocList.cons a b m.1.buckets[(mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat]) ⋯ },
              ⋯⟩)).fst =
    AssocList.contains a m.val.buckets[(mkIdx m.val.buckets.size ⋯ (hash a)).val.toNat]

Tactic:
split <;> simp_all

Result:
no goals

Proof state:
α : Type u
β : α → Type v
inst✝¹ : BEq α
inst✝ : Hashable α
m : Raw₀ α β
a : α
b : β a
⊢ (m.containsThenInsert a b).fst = m.containsₘ a

Tactic:
rw [containsThenInsert, containsₘ, bucket]

Result:
α : Type u
β : α → Type v
inst✝¹ : BEq α
inst✝ : Hashable α
m : Raw₀ α β
a : α
b : β a
⊢ (match mkIdx m.1.buckets.size ⋯ (hash a) with
      | ⟨i, h⟩ =>
        let bkt := m.1.buckets[i];
        if AssocList.contains a bkt = true then
          let buckets' := m.1.buckets.uset i AssocList.nil h;
          (true, ⟨{ size := m.1.size, buckets := buckets'.uset i (AssocList.replace a b bkt) ⋯ }, ⋯⟩)
        else
          let size' := m.1.size + 1;
          let buckets' := m.1.buckets.uset i (AssocList.cons a b bkt) h;
          (false, expandIfNecessary ⟨{ size := size', buckets := buckets' }, ⋯⟩)).fst =
    AssocList.contains a
      (match mkIdx m.val.buckets.size ⋯ (hash a) with
      | ⟨i, h⟩ => m.val.buckets[i])