theorem nonuniformWitnesses_spec (h : ¬G.IsUniform ε s t) :
    ε ≤
      |G.edgeDensity (G.nonuniformWitnesses ε s t).1 (G.nonuniformWitnesses ε s t).2 -
          G.edgeDensity s t| := by
  rw [nonuniformWitnesses, dif_pos h]
  

Proof state:
α : Type u_1
𝕜 : Type u_2
inst✝¹ : LinearOrderedField 𝕜
G : SimpleGraph α
inst✝ : DecidableRel G.Adj
ε : 𝕜
s t : Finset α
a b : α
h : ¬IsUniform G ε s t
⊢ ε ≤
    ↑|edgeDensity G
            (Exists.choose
                  (_ :
                    ∃ s' ⊆ s,
                      ∃ t' ⊆ t,
                        ↑(card s) * ε ≤ ↑(card s') ∧
                          ↑(card t) * ε ≤ ↑(card t') ∧ ε ≤ ↑|edgeDensity G s' t' - edgeDensity G s t|),
                Exists.choose
                  (_ :
                    ∃ t' ⊆ t,
                      ↑(card s) * ε ≤
                          ↑(card
                              (Exists.choose
                                (_ :
                                  ∃ s' ⊆ s,
                                    ∃ t' ⊆ t,
                                      ↑(card s) * ε ≤ ↑(card s') ∧
                                        ↑(card t) * ε ≤ ↑(card t') ∧ ε ≤ ↑|edgeDensity G s' t' - edgeDensity G s t|))) ∧
                        ↑(card t) * ε ≤ ↑(card t') ∧
                          ε ≤
                            ↑|edgeDensity G
                                    (Exists.choose
                                      (_ :
                                        ∃ s' ⊆ s,
                                          ∃ t' ⊆ t,
                                            ↑(card s) * ε ≤ ↑(card s') ∧
                                              ↑(card t) * ε ≤ ↑(card t') ∧
                                                ε ≤ ↑|edgeDensity G s' t' - edgeDensity G s t|))
                                    t' -
                                  edgeDensity G s t|)).1
            (Exists.choose
                  (_ :
                    ∃ s' ⊆ s,
                      ∃ t' ⊆ t,
                        ↑(card s) * ε ≤ ↑(card s') ∧
                          ↑(card t) * ε ≤ ↑(card t') ∧ ε ≤ ↑|edgeDensity G s' t' - edgeDensity G s t|),
                Exists.choose
                  (_ :
                    ∃ t' ⊆ t,
                      ↑(card s) * ε ≤
                          ↑(card
                              (Exists.choose
                                (_ :
                                  ∃ s' ⊆ s,
                                    ∃ t' ⊆ t,
                                      ↑(card s) * ε ≤ ↑(card s') ∧
                                        ↑(card t) * ε ≤ ↑(card t') ∧ ε ≤ ↑|edgeDensity G s' t' - edgeDensity G s t|))) ∧
                        ↑(card t) * ε ≤ ↑(card t') ∧
                          ε ≤
                            ↑|edgeDensity G
                                    (Exists.choose
                                      (_ :
                                        ∃ s' ⊆ s,
                                          ∃ t' ⊆ t,
                                            ↑(card s) * ε ≤ ↑(card s') ∧
                                              ↑(card t) * ε ≤ ↑(card t') ∧
                                                ε ≤ ↑|edgeDensity G s' t' - edgeDensity G s t|))
                                    t' -
                                  edgeDensity G s t|)).2 -
          edgeDensity G s t|

Next tactic:
exact (not_isUniform_iff.1 h).choose_spec.2.choose_spec.2.2.2