Theorems · Theorem · real analysis
NNReal.coe_nonneg
∀ (r : NNReal), 0 ≤ ↑r
- Defined in
- Mathlib.Data.NNReal.Defs
- Cited by
- 130 results in Mathlib
- Foundations
- Depth 97 from the axioms, rests on 1,954 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement · cited by 1,260
Cited by130
Results whose statement or proof uses this declaration.
- Real.sqrt_nonnegproof · cited by 35
- MeasureTheory.lintegral_coe_eq_integralproof · cited by 11
- SpectrumRestricts.nnreal_iffproof · cited by 8
- FormalMultilinearSeries.summable_norm_mul_powproof · cited by 5
- integral_withDensity_eq_integral_smulproof · cited by 4
- Metric.closedEBall_coeproof · cited by 4
- HolderOnWith.edist_le_of_leproof · cited by 4
- Measure.ext_of_integral_prod_mul_prod_boundedContinuousFunctionproof · cited by 4
- FormalMultilinearSeries.div_le_radius_compContinuousLinearMapproof · cited by 3
- FormalMultilinearSeries.isLittleO_of_lt_radiusproof · cited by 3
- ODE.FunSpace.mem_closedBallproof · cited by 3