theorem extracted_formal_statement_13 (a : NNReal) (ha : ↑a > 0) (b : NNReal) (hb : ↑b < ⊤)
  (hm : 1 ≤ ENNReal.ofReal ↑a * ↑b) : ↑a * (↑b).toReal ≥ 1 := sorry

State before:
case intro.intro
a : NNReal
ha : ↑a > 0
b : NNReal
hb : ↑b < ⊤
hm : 1 ≤ ENNReal.ofReal ↑a * ↑b
⊢ ↑a * (↑b).toReal ≥ 1

Tactic: simp at hm
    simp
    rw [← NNReal.coe_mul]
    rw [← ENNReal.coe_mul] at hm
    rwa [ENNReal.one_le_coe_iff] at hm

State after:

Relevant lemmas:
NNReal.coe_mul : ∀ (r₁ r₂ : NNReal), ↑(r₁ * r₂) = ↑r₁ * ↑r₂
ENNReal.coe_mul : ∀ (x y : NNReal), ↑(x * y) = ↑x * ↑y
ENNReal.one_le_coe_iff : ∀ {r : NNReal}, 1 ≤ ↑r ↔ 1 ≤ r