ofReal_le_iff_le_toReal — Mathlib

English

For r ∈ ℝ and n ∈ ℕ with n ≥ 2, ENNReal.ofReal r = ofNat(n) iff r = n.cast.

Русский

Для r ∈ ℝ и n ∈ ℕ, n ≥ 2: ENNReal.ofReal r = ofNat(n) тогда и только если r = n.cast.

LaTeX

$$$ ENNReal.ofReal r = ofNat(n) \iff r = n.cast $$$

Lean4

theorem ofReal_le_iff_le_toReal {a : ℝ} {b : ℝ≥0∞} (hb : b ≠ ∞) : ENNReal.ofReal a ≤ b ↔ a ≤ ENNReal.toReal b :=
  by
  lift b to ℝ≥0 using hb
  simpa [ENNReal.ofReal, ENNReal.toReal] using Real.toNNReal_le_iff_le_coe

Похожие утверждения