Theorems · Theorem · real analysis
Mathlib.Meta.Positivity.nnreal_coe_pos
∀ {r : NNReal}, 0 < r → 0 < ↑rAlias of the reverse direction of NNReal.coe_pos.
- Defined in
- Mathlib.Data.NNReal.Defs
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 106 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 · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement · cited by 1,260
- NNReal.coe_posproof · cited by 31
Cited by31
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleOTVS_iff_isLittleOproof · cited by 7
- ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mulproof · cited by 4
- ProbabilityTheory.integrable_gaussianPDFRealproof · cited by 4
- ProbabilityTheory.complexMGF_id_gaussianRealproof · cited by 3
- FormalMultilinearSeries.ofScalars_radius_eq_top_of_tendstoproof · cited by 3
- HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principalproof · cited by 3
- Asymptotics.isBigOTVS_iff_isBigOproof · cited by 3
- IsOpen.exists_contDiff_support_eqproof · cited by 2
- ProbabilityTheory.integral_cauchyPDFReal_eq_oneproof · cited by 2
- ProbabilityTheory.lintegral_gaussianPDFReal_eq_oneproof · cited by 2
- FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendstoproof · cited by 2
- HolderOnWith.of_leproof · cited by 2