one_lt_ofReal — Mathlib

English

For a ∈ ℝ, b ∈ ENNReal with b ≠ ∞ and a ≥ 0, we have ENNReal.ofReal a < b iff a < ENNReal.toReal b.

Русский

Для a ∈ ℝ, b ∈ ENNReal, b ≠ ∞ и a ≥ 0: ENNReal.ofReal a < b ⇔ a < ENNReal.toReal b.

LaTeX

$$$ (a \in \mathbb{R}, b \in \mathrm{ENNReal}, a \ge 0, b \neq \infty) \Rightarrow ENNReal.ofReal a < b \iff a < ENNReal.toReal b $$$

Lean4

@[simp]
theorem one_lt_ofReal {r : ℝ} : 1 < ENNReal.ofReal r ↔ 1 < r :=
  coe_lt_coe.trans Real.one_lt_toNNReal

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