Theorems · Theorem · real analysis
Real.sqrt_pos_of_pos
∀ {x : ℝ}, 0 < x → 0 < √xAlias of the reverse direction of Real.sqrt_pos.
- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 130 from the axioms · 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 and proof · cited by 25,697
- Real.sqrtstatement · cited by 545
- Real.sqrt_posproof · cited by 16
Cited by50
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Fernique.logRatio_posproof · cited by 4
- Stirling.log_stirlingSeq_sdiff_leproof · cited by 3
- UpperHalfPlane.cosh_half_distproof · cited by 3
- Real.strictMonoOn_artanhproof · cited by 2
- Real.abs_mulExpNegMulSq_leproof · cited by 2
- ProbabilityTheory.lintegral_gaussianPDFReal_eq_oneproof · cited by 2
- Chebyshev.abs_psi_sub_theta_le_sqrt_mul_logproof · cited by 2
- integral_gaussianproof · cited by 2
- ProbabilityTheory.gaussianPDFReal_inv_mulproof · cited by 2
- Stirling.stirlingSeq'_posproof · cited by 2
- EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radiusproof · cited by 2
- InnerProductSpace.volume_ball_of_dim_oddproof · cited by 2