Theorems · Theorem · real analysis
Real.toNNReal_le_iff_le_coe
∀ {r : ℝ} {p : NNReal}, r.toNNReal ≤ p ↔ r ≤ ↑p- Defined in
- Mathlib.Data.NNReal.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement · cited by 1,260
- Real.toNNRealstatement · cited by 267
- GaloisInsertion.gcproof · cited by 137
- NNReal.giproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- ENNReal.ofReal_le_iff_le_toRealproof · cited by 10
- SchwartzMap.eLpNorm_le_seminormproof · cited by 2
- Real.lt_toNNReal_iff_coe_ltproof · cited by 2
- MeasureTheory.eLpNorm_one_le_of_leproof · cited by 1
- NNReal.toReal_liminfproof · cited by 1
- NNReal.toReal_limsupproof · cited by 1
- MeasureTheory.lintegral_coe_le_coe_iff_integral_leproof · cited by 1
- Set.OrdConnected.image_real_toNNRealproof · cited by 1
- NNReal.tendsto_rpow_atTopproof · cited by 1