Theorems · Theorem · real analysis
Real.sqrt_sq
∀ {x : ℝ}, 0 ≤ x → √(x ^ 2) = x- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 129 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
- Real.sqrtstatement and proof · cited by 545
- sqproof · cited by 280
- Real.sqrt_mul_selfproof · cited by 14
Cited by36
Results whose statement or proof uses this declaration.
- Complex.cos_argproof · cited by 7
- norm_eq_sqrt_re_innerproof · cited by 5
- InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zeroproof · cited by 5
- Real.lt_sqrtproof · cited by 4
- contDiffAt_normproof · cited by 4
- Real.sqrt_ltproof · cited by 4
- InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zeroproof · cited by 4
- RKHS.norm_kerFun_eq_sqrt_norm_kernelproof · cited by 3
- ContinuousLinearMap.norm_adjoint_comp_selfproof · cited by 3
- Real.cosh_arsinhproof · cited by 2
- Complex.norm_le_sqrt_two_mul_maxproof · cited by 2
- Real.cos_halfproof · cited by 2