-- Mathlib/.lake/packages/lean4/src/lean/Std/Data/DHashMap/Internal/Model.lean
theorem containsThenInsertIfNew_eq_insertIfNewₘ [BEq α] [Hashable α] (m : Raw₀ α β) (a : α)
    (b : β a) : (m.containsThenInsertIfNew a b).2 = m.insertIfNewₘ a b

Proof state:
case isFalse
α : Type u
β : α → Type v
inst✝¹ : BEq α
inst✝ : Hashable α
m : Raw₀ α β
a : α
b : β a
h✝ : ¬AssocList.contains a m.1.buckets[(mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat] = true
⊢ (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]) ⋯ },
            ⋯⟩).snd =
    (m.consₘ a b).expandIfNecessary

Tactic:
rfl

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
⊢ (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 }, ⋯⟩)
      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]) ⋯ },
              ⋯⟩)).snd =
    if AssocList.contains a m.val.buckets[(mkIdx m.val.buckets.size ⋯ (hash a)).val.toNat] = true then m
    else (m.consₘ a b).expandIfNecessary

Tactic:
split

Result:
case isTrue
α : Type u
β : α → Type v
inst✝¹ : BEq α
inst✝ : Hashable α
m : Raw₀ α β
a : α
b : β a
h✝ : AssocList.contains a m.1.buckets[(mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat] = true
⊢ (true, ⟨{ size := m.1.size, buckets := m.1.buckets }, ⋯⟩).snd = m

case isFalse
α : Type u
β : α → Type v
inst✝¹ : BEq α
inst✝ : Hashable α
m : Raw₀ α β
a : α
b : β a
h✝ : ¬AssocList.contains a m.1.buckets[(mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat] = true
⊢ (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]) ⋯ },
            ⋯⟩).snd =
    (m.consₘ a b).expandIfNecessary

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.containsThenInsertIfNew a b).snd = m.insertIfNewₘ a b

Tactic:
rw [containsThenInsertIfNew, insertIfNewₘ, 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 (true, ⟨{ size := m.1.size, buckets := m.1.buckets }, ⋯⟩)
        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' }, ⋯⟩)).snd =
    if
        AssocList.contains a
            (match mkIdx m.val.buckets.size ⋯ (hash a) with
            | ⟨i, h⟩ => m.val.buckets[i]) =
          true then
      m
    else (m.consₘ a b).expandIfNecessary

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 (true, ⟨{ size := m.1.size, buckets := m.1.buckets }, ⋯⟩)
        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' }, ⋯⟩)).snd =
    if
        AssocList.contains a
            (match mkIdx m.val.buckets.size ⋯ (hash a) with
            | ⟨i, h⟩ => m.val.buckets[i]) =
          true then
      m
    else (m.consₘ a b).expandIfNecessary

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 }, ⋯⟩)
      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]) ⋯ },
              ⋯⟩)).snd =
    if AssocList.contains a m.val.buckets[(mkIdx m.val.buckets.size ⋯ (hash a)).val.toNat] = true then m
    else (m.consₘ a b).expandIfNecessary

Proof state:
case isTrue
α : Type u
β : α → Type v
inst✝¹ : BEq α
inst✝ : Hashable α
m : Raw₀ α β
a : α
b : β a
h✝ : AssocList.contains a m.1.buckets[(mkIdx m.1.buckets.size ⋯ (hash a)).val.toNat] = true
⊢ (true, ⟨{ size := m.1.size, buckets := m.1.buckets }, ⋯⟩).snd = m

Tactic:
simp only [replaceₘ, Subtype.mk.injEq, Raw.mk.injEq, true_and]

Result:
no goals