have : result.2 = swapped := by
  rw [←eq]
  unfold partition
  simp [afterLoop, dbgTraceIfShared]
α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
first last : Fin n
fl : first ≤ last
result : { mid // first ≤ mid ∧ mid ≤ last } × Vec α n
eq : _root_.partition arr first last fl = result
afterLoop : { mid // first ≤ mid ∧ mid ≤ last } × Vec α n := partitionImpl arr first last last fl ⋯
mid : { mid // first ≤ mid ∧ mid ≤ last } := afterLoop.fst
arr' : Vec α n := afterLoop.snd
this✝ : ↑mid.val < n
swapped : Vec α n := arr'.swap first ⟨↑mid.val, this✝⟩
this : result.fst = mid
⊢ (∀ (k : Fin n), first ≤ k → ↑k < ↑result.fst.val → result.snd[k] < arr[first]) ∧
    result.snd[result.fst.val] = arr[first] ∧
      ∀ (k : Fin n), ↑result.fst.val < ↑k → k ≤ last → ¬result.snd[k] < arr[first]
α : Type
inst✝ : Ord α
n : Nat
arr : Vec α n
first last : Fin n
fl : first ≤ last
result : { mid // first ≤ mid ∧ mid ≤ last } × Vec α n
eq : _root_.partition arr first last fl = result
afterLoop : { mid // first ≤ mid ∧ mid ≤ last } × Vec α n := partitionImpl arr first last last fl ⋯
mid : { mid // first ≤ mid ∧ mid ≤ last } := afterLoop.fst
arr' : Vec α n := afterLoop.snd
this✝¹ : ↑mid.val < n
swapped : Vec α n := arr'.swap first ⟨↑mid.val, this✝¹⟩
this✝ : result.fst = mid
this : result.snd = swapped
⊢ (∀ (k : Fin n), first ≤ k → ↑k < ↑result.fst.val → result.snd[k] < arr[first]) ∧
    result.snd[result.fst.val] = arr[first] ∧
      ∀ (k : Fin n), ↑result.fst.val < ↑k → k ≤ last → ¬result.snd[k] < arr[first]