Theorems · Theorem · real analysis
Real.sqrt_mul_self
∀ {x : ℝ}, 0 ≤ x → √(x * x) = x- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- mul_self_nonnegproof · cited by 35
- Real.sqrt_nonnegproof · cited by 35
- Real.mul_self_sqrtproof · cited by 23
- mul_self_inj_of_nonnegproof · cited by 9
Cited by14
Results whose statement or proof uses this declaration.
- Real.sqrt_sqproof · cited by 36
- inner_self_eq_norm_mul_normproof · cited by 9
- Real.cos_arcsinproof · cited by 4
- Real.sqrt_mul_self_eq_absproof · cited by 4
- Real.sqrt_eq_iff_mul_self_eqproof · cited by 3
- ContinuousLinearMap.norm_adjoint_comp_selfproof · cited by 3
- Real.cos_pi_div_sixproof · cited by 3
- InnerProductGeometry.angle_add_pos_of_inner_eq_zeroproof · cited by 2
- RCLike.norm_of_nonneg'proof · cited by 1
- ContinuousLinearMap.isPositive_iff_eq_sum_rankOneproof · cited by 1
- CStarModule.normedSpaceCoreproof · cited by 1
- InnerProductSpace.Core.inner_self_eq_norm_mul_normproof · cited by 1