Theorems · Theorem · real analysis
Real.sqrt_mul_self_eq_abs
∀ (x : ℝ), √(x * x) = |x|
- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 4 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.
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
- absstatement and proof · cited by 1,814
- Real.sqrtstatement and proof · cited by 545
- abs_nonnegproof · cited by 168
- abs_mul_abs_selfproof · cited by 21
- Real.sqrt_mul_selfproof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- Complex.norm_realproof · cited by 105
- Real.sqrt_sq_eq_absproof · cited by 13
- irrational_sqrt_ratCast_iff_of_nonnegproof · cited by 3
- UpperHalfPlane.isometry_pos_mulproof · cited by 0