theorem unitsSMul_neg (u : ℤˣ) (w : NormalWord d) :
    unitsSMul φ (-u) (unitsSMul φ u w) = w := by
  rw [unitsSMul]
  split_ifs with hcan
  · have hncan : ¬ Cancels u w := (unitsSMul_cancels_iff _ _ _).1 hcan
    unfold unitsSMul
    simp only [dif_neg hncan]
    simp [unitsSMulWithCancel, unitsSMulGroup, (d.compl u).equiv_snd_eq_inv_mul]
    -- This used to be the end of the proof before leanprover/lean4#2644
    erw [(d.compl u).equiv_snd_eq_inv_mul]
    simp
  · have hcan2 : Cancels u w := not_not.1 (mt (unitsSMul_cancels_iff _ _ _).2 hcan)
    unfold unitsSMul at hcan ⊢
    simp only [dif_pos hcan2] at hcan ⊢
    

Proof state:
case neg
G : Type u_1
inst✝³ : Group G
A B : Subgroup G
φ : ↥A ≃* ↥B
H : Type u_2
inst✝² : Group H
M : Type u_3
inst✝¹ : Monoid M
d : TransversalPair G A B
inst✝ : DecidableEq G
u : ℤˣ
w : NormalWord d
hcan✝ :
  ¬Cancels (-u)
      (if h : Cancels u w then unitsSMulWithCancel φ u w h
      else
        let g' := unitsSMulGroup φ d u w.head;
        cons (↑g'.1) u ((↑g'.2 * w.head⁻¹) • w)
          (_ : ↑(unitsSMulGroup φ d u w.head).2 * w.head⁻¹ * w.head ∈ TransversalPair.set d u)
          (_ :
            ∀ u' ∈ Option.map Prod.fst (List.head? ((↑(unitsSMulGroup φ d u w.head).2 * w.head⁻¹) • w).toList),
              ((↑(unitsSMulGroup φ d u w.head).2 * w.head⁻¹) • w).head ∈ toSubgroup A B u → u = u'))
hcan2 : Cancels u w
hcan : ¬Cancels (-u) (unitsSMulWithCancel φ u w hcan2)
⊢ cons (↑(unitsSMulGroup φ d (-u) (unitsSMulWithCancel φ u w hcan2).toReducedWord.head).1) (-u)
      ((↑(unitsSMulGroup φ d (-u) (unitsSMulWithCancel φ u w hcan2).toReducedWord.head).2 *
          (unitsSMulWithCancel φ u w hcan2).toReducedWord.head⁻¹) •
        unitsSMulWithCancel φ u w hcan2)
      (_ :
        ((↑(unitsSMulGroup φ d (-u) (unitsSMulWithCancel φ u w hcan2).toReducedWord.head).2 *
                (unitsSMulWithCancel φ u w hcan2).toReducedWord.head⁻¹) •
              unitsSMulWithCancel φ u w hcan2).head ∈
          TransversalPair.set d (-u))
      (_ :
        ∀
          u' ∈
            Option.map Prod.fst
              (List.head?
                ((↑(unitsSMulGroup φ d (-u) (unitsSMulWithCancel φ u w hcan2).toReducedWord.head).2 *
                      (unitsSMulWithCancel φ u w hcan2).toReducedWord.head⁻¹) •
                    unitsSMulWithCancel φ u w hcan2).toList),
          ((↑(unitsSMulGroup φ d (-u) (unitsSMulWithCancel φ u w hcan2).toReducedWord.head).2 *
                    (unitsSMulWithCancel φ u w hcan2).toReducedWord.head⁻¹) •
                  unitsSMulWithCancel φ u w hcan2).head ∈
              toSubgroup A B (-u) →
            -u = u') =
    w

Next tactic:
cases w using consRecOn with
    | ofGroup => simp [Cancels] at hcan2
    | cons g u' w h1 h2 ih =>
      clear ih
      simp only [unitsSMulGroup, SetLike.coe_sort_coe, unitsSMulWithCancel, id_eq, consRecOn_cons,
        group_smul_head, IsComplement.equiv_mul_left, map_mul, Submonoid.coe_mul, coe_toSubmonoid,
        toSubgroupEquiv_neg_apply, mul_inv_rev]
      cases hcan2.2
      have : ((d.compl (-u)).equiv w.head).1 = 1 :=
        (d.compl (-u)).equiv_fst_eq_one_of_mem_of_one_mem _ h1
      apply NormalWord.ext
      · -- This used to `simp [this]` before leanprover/lean4#2644
        dsimp
        conv_lhs => erw [IsComplement.equiv_mul_left]
        rw [map_mul, Submonoid.coe_mul, toSubgroupEquiv_neg_apply, this]
        simp
      · -- The next two lines were not needed before leanprover/lean4#2644
        dsimp
        conv_lhs => erw [IsComplement.equiv_mul_left]
        simp [mul_assoc, Units.ext_iff, (d.compl (-u)).equiv_snd_eq_inv_mul, this]
        -- The next two lines were not needed before leanprover/lean4#2644
        erw [(d.compl (-u)).equiv_snd_eq_inv_mul, this]
        simp