Theorems · Theorem · real analysis
Real.coe_toNNReal
∀ (r : ℝ), 0 ≤ r → ↑r.toNNReal = r
- Defined in
- Mathlib.Data.NNReal.Defs
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- NNReal.toRealstatement · cited by 1,260
- Real.toNNRealstatement · cited by 267
- max_eq_leftproof · cited by 96
Cited by27
Results whose statement or proof uses this declaration.
- Real.mul_self_sqrtproof · cited by 23
- Real.toNNReal_oneproof · cited by 13
- Real.toNNReal_zeroproof · cited by 9
- Real.toNNReal_natCastproof · cited by 7
- Real.nnabs_of_nonnegproof · cited by 6
- MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smulproof · cited by 6
- Real.le_toNNReal_iff_coe_leproof · cited by 5
- Real.toNNReal_invproof · cited by 5
- ProbabilityTheory.isGaussian_iff_gaussian_charFunDualproof · cited by 4
- Height.mulHeight_powproof · cited by 3
- Real.toNNReal_eq_iff_eq_coeproof · cited by 2
- MeasureTheory.integrableOn_image_iff_integrableOn_abs_det_fderiv_smulproof · cited by 2