theorem extracted_formal_statement_18.{u_1} {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E]
  {f : E → ℝ} {G : NNReal} (h : ∀ (x y : E), edist (f x) (f y) ≤ ↑G * edist x y) (x g : E) (h₂ : g ∈ SubderivAt f x)
  (h₃ : ↑G < ‖g‖) :
  let y := x + (1 / ‖g‖) • g;
  y = x + (1 / ‖g‖) • g →
    f y ≥ f x + ‖g‖ →
      ‖g‖ ≠ 0 →
        ⟪g, y - x⟫_ℝ = ‖g‖ → f y - f x ≥ ‖g‖ → edist (f x) (f y) ≤ ↑G * edist x y → ↑G = ENNReal.ofReal ↑G := sorry

State before:
E : Type u_1
inst✝¹ : NormedAddCommGroup E
inst✝ : InnerProductSpace ℝ E
f : E → ℝ
G : NNReal
h : ∀ (x y : E), edist (f x) (f y) ≤ ↑G * edist x y
x g : E
h₂ : g ∈ SubderivAt f x
h₃ : ↑G < ‖g‖
y : E := x + (1 / ‖g‖) • g
hy : y = x + (1 / ‖g‖) • g
hy₂ : f y ≥ f x + ‖g‖
hg₁ : ‖g‖ ≠ 0
hl : ⟪g, y - x⟫_ℝ = ‖g‖
x✝ : f y - f x ≥ ‖g‖
h₅ : edist (f x) (f y) ≤ ↑G * edist x y
⊢ ↑G = ENNReal.ofReal ↑G

Tactic: rw [ENNReal.ofReal_coe_nnreal]

State after:

Relevant lemmas:
ENNReal.ofReal_coe_nnreal : ∀ {p : NNReal}, ENNReal.ofReal ↑p = ↑p