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 ⊢
    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]
      

Proof state:
case neg.cons
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
g : G
u' : ℤˣ
w : NormalWord d
h1 : w.head ∈ TransversalPair.set d u'
h2 : ∀ u'_1 ∈ Option.map Prod.fst (List.head? w.toList), w.head ∈ toSubgroup A B u' → u' = u'_1
hcan✝ :
  ¬Cancels (-u)
      (if h : Cancels u (cons g u' w h1 h2) then unitsSMulWithCancel φ u (cons g u' w h1 h2) h
      else
        let g' := unitsSMulGroup φ d u (cons g u' w h1 h2).toReducedWord.head;
        cons (↑g'.1) u ((↑g'.2 * (cons g u' w h1 h2).toReducedWord.head⁻¹) • cons g u' w h1 h2)
          (_ :
            ↑(unitsSMulGroup φ d u (cons g u' w h1 h2).toReducedWord.head).2 *
                  (cons g u' w h1 h2).toReducedWord.head⁻¹ *
                (cons g u' w h1 h2).toReducedWord.head ∈
              TransversalPair.set d u)
          (_ :
            ∀
              u'_1 ∈
                Option.map Prod.fst
                  (List.head?
                    ((↑(unitsSMulGroup φ d u (cons g u' w h1 h2).toReducedWord.head).2 *
                          (cons g u' w h1 h2).toReducedWord.head⁻¹) •
                        cons g u' w h1 h2).toList),
              ((↑(unitsSMulGroup φ d u (cons g u' w h1 h2).toReducedWord.head).2 *
                        (cons g u' w h1 h2).toReducedWord.head⁻¹) •
                      cons g u' w h1 h2).head ∈
                  toSubgroup A B u →
                u = u'_1))
hcan2 : Cancels u (cons g u' w h1 h2)
hcan : ¬Cancels (-u) (unitsSMulWithCancel φ u (cons g u' w h1 h2) hcan2)
⊢ cons
      (↑((toSubgroupEquiv φ (-u))
          ((IsComplement.equiv (_ : IsComplement (↑(toSubgroup A B (-u))) (TransversalPair.set d (-u))))
              (↑((toSubgroupEquiv φ u)
                    { val := g, property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }) *
                w.head)).1))
      (-u)
      ((↑((IsComplement.equiv (_ : IsComplement (↑(toSubgroup A B (-u))) (TransversalPair.set d (-u))))
                (↑((toSubgroupEquiv φ u)
                      { val := g, property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }) *
                  w.head)).2 *
          (w.head⁻¹ *
            (↑((toSubgroupEquiv φ u)
                  { val := g, property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }))⁻¹)) •
        ↑((toSubgroupEquiv φ u)
              { val := g, property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }) •
          w)
      (_ :
        ((↑((IsComplement.equiv (_ : IsComplement (↑(toSubgroup A B (-u))) (TransversalPair.set d (-u))))
                      (↑((toSubgroupEquiv φ u)
                            { val := g, property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }) *
                        w.head)).2 *
                (w.head⁻¹ *
                  (↑((toSubgroupEquiv φ u)
                        { val := g,
                          property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }))⁻¹)) •
              ↑((toSubgroupEquiv φ u)
                    { val := g, property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }) •
                w).head ∈
          TransversalPair.set d (-u))
      (_ :
        ∀
          u'_1 ∈
            Option.map Prod.fst
              (List.head?
                ((↑((IsComplement.equiv (_ : IsComplement (↑(toSubgroup A B (-u))) (TransversalPair.set d (-u))))
                            (↑((toSubgroupEquiv φ u)
                                  { val := g,
                                    property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }) *
                              w.head)).2 *
                      (w.head⁻¹ *
                        (↑((toSubgroupEquiv φ u)
                              { val := g,
                                property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }))⁻¹)) •
                    ↑((toSubgroupEquiv φ u)
                          { val := g, property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }) •
                      w).toList),
          ((↑((IsComplement.equiv (_ : IsComplement (↑(toSubgroup A B (-u))) (TransversalPair.set d (-u))))
                          (↑((toSubgroupEquiv φ u)
                                { val := g,
                                  property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }) *
                            w.head)).2 *
                    (w.head⁻¹ *
                      (↑((toSubgroupEquiv φ u)
                            { val := g,
                              property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }))⁻¹)) •
                  ↑((toSubgroupEquiv φ u)
                        { val := g, property := (_ : (cons g u' w h1 h2).toReducedWord.head ∈ toSubgroup A B u) }) •
                    w).head ∈
              toSubgroup A B (-u) →
            -u = u'_1) =
    cons g u' w h1 h2

Next tactic:
cases hcan2.2